However, the folks on the Giant in the Playground forums have rewritten the class in an attempt to mold the Truenamer into something useful. What Tier is the GitP re-engineered Truenamer in? Does it get bumped up to tier 3-4? Does it make it all the way up to tier 1-2 where full casters sit?
The point of TWWW is to remove the parts of Truenaming that don't work, improve the parts that are crappy, and get rid of the parts that are hilariously broken. In general, it seems to have done this, with a few exceptions. There are definitely still some options that are clearly better, and some that are clearly worse, but TWWW is definitely more balanced than the ToM Truenamer.
TL;DR The Truenamer and Lexeme are both Tier 3 until level 16, when they are Tier 2. A high-optimization player can probably get a 15th or lower level Truenamer or Lexeme into Tier 2-like levels of power, though I can't see any obvious ways. If you remove Rebuild the Dweomer and Rewrite the World, then the Truenamer and Lexeme are Tier 3 throughout.
Throughout this post, I will use the term "Truenamer" to refer to the class, and "truenamer" to refer to any character who can make vocalizations. the TWWW glossary doesn't give a good general adjective to describe all truenaming characters, so I'm just going to use a lower-case version of the class name.
The max bonus to truespeak checks is still pretty high
One of the big changes in TWWW is that it's a lot more difficult to gain bonuses to truespeak checks. However, you can still get a bonus of roughly +60 at level 20. There is no mention of removing the Paragnostic assembly, and you can still get a bunch of feat bonuses. In this analysis, I'm assuming that all of the tricks listed in the truenamer handbook work, unless specifically denied. Here's my math for a level 20 Lexeme:
Skill Focus: +3
Illumian Race: +2
Favored: Paragnostic Assembly: +2
Affiliation 23 with Paragnostic Assembly: +10
10 languages known: +5
Confident Speaker: +10
Skill Ranks: +23
Total Bonus: +62
All of these bonuses are untyped, except the bonus for languages known (synergy) and the bonus for Confident Speaker (competence). You can almost certainly find ways to increase it further, but for this analysis, I'll assume a +64 check is doable.
Offensive utterances are largely useless
Offensive utterances are usually really powerful, and are pretty easy to buff to crazy levels, but they have one big problem: the absolute limit. A truenamer has an absolute limit of 1+Cha per level, which doesn't apply retroactively with later Cha buffs. Since Cha is, at best, a secondary stat for truenamers, this is unlikely to be very high. Assuming you start with a Cha around 14 and end around 20, you'll end up with an absolute limit of about 90 by level 20. If you augment the utterance to it's maximum, the limit only goes up to 110. For a level 20 party, 110 hit points is the level where you can pretty easily kill an enemy in one round, if not a single attack. It's going to be very rare that a truenamer will be able to effectively use an offensive utterance.
Buff utterances range from lackluster to powerful
On the low end of power, you have things like the Phrase of Balance, which gives a +4 bonus to bull rush and trip resistance, and can let you stand up from prone as a free action. In the middle, you have things like the Phrase of Perfection (+2 to 9 bonus to one stat), the Phrase of Flight (grants a fly speed (average) that's anywhere from the same as land speed to triple land speed), or the Phrase of Battle (+1 to 11 bonus to melee attack and damage rolls). At the high end, there's the Phrase of Temporal Acceleration (for 5 rounds, the target gets an extra standard or full-round action). There are a few 'utility' utterances that are cool, but hardly game-breaking. The Syllable of Death is a free raise dead without negative levels, xp costs, or material components, and the Syllable of Tesseract is teleport, but with no range limit and the ability to teleport places you've never been. The Phrase of Temporal Acceleration might cause some action economy issues, but there's really nothing here that would break a game in the way that high-level wizards can.
There are two kinds of incantations: interesting, and wish
Most of the incantations give random-seeming spell effects that generally look pretty interesting. There's an incantation that works like passwall, one that's like purify food and drink, one that's like heat metal, and even one that makes it snow in a 10 foot radius. Generally, you get any particular effect either at the same time as a primary caster, or a few levels later.
There are two incantation which break this pattern, Rebuild the Dweomer and Rewrite the World. Rebuild the Dweomer lets you restore a magic item to whatever state it was in 1 round ago. This lets you recharge a wand, undrink a potion, or un-wish a ring of three wishes. I shudder to think of what you could do with a Thought Bottle. With this incantation and a scroll of simulacrum, true ressurection, or wish, you can end up with an unending supply of powerful magic.
The other incantation that breaks this pattern is even more powerful: Rewrite the World. Rewrite the World is a DC 60 incantation that replicates wish, without the normal costs associated with it. Every time you use it, it gives you a -5 to further Truename checks that day. With a +62 to your Truename check, this means that you can have 3 wishes per day before you have to seriously worry about failing a check. If you can get by the 'no magic item or spell bonuses to your truespeak checks', which I'd almost guarantee is possible given the size of the 3.5 ruleset, you can make wishes all day long. This incantation establishes a minimum tier of 2 once the truenamer hits level 16.
Recitations are interesting, cost too much to be game-breaking
Recitations are compared with martial stances from the Tome of Battle, and they work pretty similarly. The one big issue is that you generally can't use other truenamer powers while using a recitation, so even the more powerful ones aren't going to be that great. For example: You need to be a 10th level truenamer in order to learn Recitation of the Untouched Snow (invisibility at DC 25, greater invisibility at 41), which limits how much power you can get out of permanent invisibilty. On of the recitations, the Recitation of the Unclouded Eye, is basically essential (truenamers get it as a class feature, though lexeme's don't). It lets you know the HP of anyone you can see, thus letting oyu know if your utterances are going to work. On of the more interesting ones gives fast healing 5 (up to 10 with augmentation), but that's not enough to make a big difference in combat, so it basically just saves you some low-level healing spells.
To compare the TWWW Truenamer and Lexeme to the original tier system description of Tier 3:
Tier 3: Capable of doing one thing quite well, while still being useful when that one thing is inappropriate, or capable of doing all things, but not as well as classes that specialize in that area. Occasionally has a mechanical ability that can solve an encounter, but this is relatively rare and easy to deal with. Challenging such a character takes some thought from the DM, but isn't too difficult. Will outshine any Tier 5s in the party much of the time.
Generally, truenamers are pretty versatile, low-power spellcasters. A creative or optimization-focused player will be able to do some really awesome things, and even a low-op player will be able to make certain expensive tasks trivial. If you were to add a truenamer to an existing party, they would probably gravitate to a support/utility caster role, while still being able to dish out a little bit of damage in a pinch.
This is, of course, assuming that you aren't allowing Rebuild the Dweomer and Rewrite the World. Either of those incantations makes a truenamer an infinite cash factory at level 16, which instantly pushes them into Tier 2, regardless of other factors.
The only thing that really didn't work with the True Namer was the rapidly scaling DC as you leveled and the Law of Resistance aspect of Truenaming, both of which have been done away with. In exchange however the class has gone from an average base attack bonus to a poor one.
While the early utterances, incantations, and recitations are generally pretty balanced, when you get to the later levels things get kind of crazy. Because the writer removed the Law of Resistance and the DC is based on what you're casting rather than the Hit Dice of the creature you're trying to affect you can use your utterances every round without any downside. This can get pretty ridiculous later on when you're throwing out at-will teleportation, flying, self healing and ultimately, save or dies. Even the 1st level abilities get super crazy later on through the augmentation system. The base DC for word of battle for instance is 13 and the bonus increases by 1 for every 2 you increase the DC, for a smaller DC than you need for a level 5 utterance you can be granting your ally a +10 truespeak bonus on attack and damage rolls with melee weapons that lasts for a while.
This new revision to the truespeaker gives it a major power bump and though it isn't quite as versatile as traditional prepared casters it definitely has a lot of versatility at its disposal. I'd place it on tier 2.