Well, it is possible to gate any specific balor (i.e. Bob the Balor) in atleast the same way you can gate deities or unique creatures. That is, they can choose to come through if they desire, even if you can't compel them. The spell mentions no mechanism for 'ambiguous naming,' and it specifically states... "you cause the gate to open in the immediate vicinity of the
desired creature." It does not say, "in the immediate vicinity of a creature with the name you called." Presumably, the spell reads your intentions and the act of naming is symbolic. This, is of course, my fluff interpretation. Mechanically, fluff explanation doesn't matter - what matters is, as written, you get the desired creature, even if the name is not sufficient to be uniquely identifying.
Now onto the matter of particularity and uniqueness and gate... The gate spell mentions three classes of things it can summon, and each behaves differently.
1) Particular beings (summon one, can be compelled and possibly commanded - the wording is bad here).
2) Particular kind of beings (summon one to many, can be compelled and commanded)
3) Deities and unique beings (summon one, cannot be compelled or commanded).
I am going to drag out some merriam-webster.com definitions. I am using the top listed definitions.
Particular, adj: "of, relating to, or being a single person or thing"
Unique, adj: "being the only one"
If you call "balor" a particular being, that is wrong, because I can bring you two balors. Since I can bring you two balors, it cannot be a particular [i.e. single] being. However, each balor is individually a particular being. Particular means singular. It's right there. If you are calling something a particular being, you have to be able to look at it, point at it, and say, "there is one single being right there. It is particular." A balor is a particular kind of being though, because I can't bring you two different kinds of things which are both balors.
Furthermore, here are some of the exact quotes from the spell...
...you may then call a particular individual or kind of being through the gate...
... If you choose to call a kind of creature instead of a known individual...
The real source of confusion and problematics here is the definition of uniqueness. I am unique, in the sense that I am the only me. Bob the Balor is unique, in the sense that he is the only Bob the Balor (someone sharing the name doesn't mean they share his uniqueness, they have their own uniqueness with one trait in common). But Bob is not unique in the sense that he is the only balor.
The first definition of unique causes the spell to contradict itself in the span of two sentences - you can compel particular individuals, you cannot compel unique individuals. If unique == particular, that's stupid. So it has to be the second definition of unique - unique means "only one of its kind." Which is also a dumb definition on their part, but the only one that makes any sense.
Interesting side note: it may turn out that you can't control known individuals. Here is the text where it talks about controlling:
If you choose to call a kind of creature instead of a known individual you may call either a single creature (of any HD) or several creatures. You can call and control several creatures as long as their HD total does not exceed your caster level. In the case of a single creature, you can control it if its HD do not exceed twice your caster level. A single creature with more HD than twice your caster level can’t be controlled.
See what I'm getting at it? The entire paragraph that talks about controlling has already specifically excluded "known individuals." And nowhere else in the spell does it talk about how to control them. The rules for controlling things via casting gate are for controlling kinds of creatures and not particular individuals.