In a RPG party, if
Tank → Front line in case the party should be dealt damage
Damage Dealer → Deals damage to enemies
Healer → Heals teammates
etc.
… what's the name of the role for the character that buffs teammates (using spells or auras)?
The term I have heard the most would be Support, as it is their role to assist the other party members.
While in a lot of system Healers double as Supports, or Supports double as Healers, they're not the same thing. It highly depends on the system, though.
For demonstration of these terms: My next character in an upcoming Pathfinder campaign is a "Rogue oriented Heal and Support". Using this exact phrasing got the message across to the group.
Of course, and I can not stress this enough, it highly depends on the system. Support is kind of a generic name to designate a lot of different things.
Healers can be considered support, and are perhaps the most essential and wide represented "sub-specialization"... Until you use a setting where there is no Healer.
Skill Monkeys in D&D/Pathfinder are "enablers" (thanks @Mast for the term - very fitting), and could be considered as Support. But I rarely saw the term Skill Monkey outside of those systems.
So yes, Support is a voluntarily broad term, that might encompass other things - but it suits the description (someone giving buff is a Support) and is commonly used enough for people to understand the role you want to play.
While Support is the most common name—found widely even outside of RPGs, as video games use it frequently as well—it may be worth noting that the official terminology for D&D 4e—the only edition of D&D to officially codify roles like this—is that such classes are “Leaders.” That terminology may be used by D&D 4e players in other systems, even non-D&D systems, so it’s worth being aware of.
For the record, the four codified roles in D&D 4e were Controller, Defender, Leader, and Striker. Striker is cognate to DPS; Leader, as stated, is about buffs (and also healing). Defender is the tank, about aggro and soaking punishment. Controller is about area-effect stuff, especially things that disrupt enemy formations, deny particular areas of the battlefield, or otherwise gets in enemies’ way—in many games, this might be considered a form of support.
In many MMORPGs I also called them Buffer, but it's my jargon for them. They don't really have a name, but if we really want to give them one the Support would be the best, but actually the Healer is a support type too. So if we want to give the most correct naming I would use some Buffer-Support, because it declares the role and the type too:
For some party they are useless, because they need time to achieve their goal, but they can help a lot. As my experience says, buffer-support are very important in every group, but if it can only buff others and nothing else, they are pretty useless. If we make it to a Buffer-DPS (low DPS but has buffer skills), than it will be the best for the team, like a Leader (e.g.: Empowering battlecries, or aura effect for the front line).
The last which can break a game is like a tank character with buffer skills. As my experience dictates they are the most unbalanced type of characters due to the high survivability with the option to buff themself more and more powerful. It could balance them if they don't have any healing or high DPS buffs, just like more and more defense.
As we see the buffer is something more like a sub-type from the other primary-roles (tank, heal, dps).
TVTropes¹ and Wikipedia both class buffing in the "Healer" role.
If you want a term specifically for a class that buffs teammates, I suggest...
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¹ Warning - your productivity will suffer if you click that link. :-)
They're a subgroup of what Treantmonk refers to as God(s), or the Controller(s) of Reality in their Guide to Playing a Wizard. It's a rather tongue in cheek breakdown of the party roles, but it's got a core of truth to it.