When gating by name, gate only gates an individually specified creature, not just a single instance of a type of creature.
The spell says (emphasis added):
When you cast this spell, you can speak the name of a specific creature (a pseudonym, title, or nickname doesn't work). If that creature is on a plane other than the one you are on, the portal opens in the named creature's immediate vicinity and draws the creature through it to the nearest unoccupied space on your side of the portal.
The phrases "name of a specific creature", "that creature", and "the named creature" all indicate the spell is referring to a single, unique individual that has been identified by name.
Contrast with the many conjuring and summoning spells, for instance conjure elemental and summon fiend, which summon a single instance of a type of creature.
Furthermore, it is going to require DM adjudication.
It's going to require adjudication because there is nothing in the rules that makes names unique.
There could be multiple creatures named "Tarphon the Devourer"; perhaps the party's barbarian is "Tarphon the Devourer", and perhaps there is also a demon from the Abyss named that, and maybe also a puppy in some city across the multiverse.
The spell says:
speak the name of a specific creature (a pseudonym, title, or nickname doesn't work)
which implies that either:
- the name is a unique identifier
- The magic knows which specific creature with that name the caster is referring to.
Either way is going to require the DM to adjudicate the effects of using the spell in this way.
Many cases, it isn't going to matter much
It might not be a big deal, the DM may just hand-wave it, and the caster, whether PC or NPC, gets what they want, and as long as it works for the game, great, and everyone's happy.
DMs and players will want to work it out ahead of time
But if you're going to use this form of the Gate spell where there's any possibility of ambiguity, you should make sure you work it out ahead of time with the DM (or the player).
It would really suck to attempt to gate a party member, only to get a demon or a puppy instead.
What's in a name?
Note the spell does not say, "true name", whatever that is, or "uniquely describe a creature", or even "full name" or "complete name" it just says "speak the name of a specific creature".
It actually doesn't help much that it says:
a pseudonym, title, or nickname doesn't work
So the spell specifically says that saying "Tarphon the Devourer, also known as Tarfy the puppy" isn't helpful in distinguishing the barbarian from the demon from the puppy.
How do you define a name? What you're usually called? What your mother called you? What's on your birth certificate?
In RL names are extremely complicated, and vary greatly across culture and time.
Such things as birth certificates are a modern invention, and even in the small portion of human existence where birth certificates are a thing, names can change for many different reasons, and individuals can have multiple names.
Not only do many creatures in D&D not have birth certificates, they weren't EVEN BORN.
In the barbarian known as "Tarphon the Devourer", perhaps at birth Tarphon was held to the sky by the parent who said "This child I name 'Tarphon the Devourer', may they rule the plains", or perhaps "the Devourer" was picked up along the way. What is the actual name? If the caretaker of the puppy writes "Tarphon the Devourer" on the water bowl, does that make it the puppy's name? And how do demons even get names?
A loose interpretation
A loose interpretation is to lean heavily on "specific" (emphasis added):
speak the name of a specific creature
So that when the caster says "Tarphon the Devourer", the magic knows whether the specific Tarphon the Devourer is the puppy or the dracolich or whatever.
It will be up to the DM to grant that the magic knows which creature the caster is referring to.
A strict interpretation
A strict interpretation is that the name must be unique, or at least locally unique, within the DM's ken. Since you can't name a specific Tarphon the Devourer, you can't gate one by name.
Again, up to DM adjudication. Without knowing how the DM will rule, the player can't know what to expect.
Finally, you can houserule something better
Gate is a 9th level spell, and it's not too much of a stretch that it will be relatively rare in most games.
If you are actually using the gate spell, and using it in this way, you can work with the DM (or the player) to come up with something that doesn't quite fit RAW, but works for your game.