I think the wording of the spell - specifically, the way the two potential groups of targets are joined - speaks against the majority here.
There are two potential target groups:
"[By naming] a particular being or kind of being"
-- and --
"Deities and unique beings"
Members of the first group are brought through whether or not they are willing - "pull the subject through, willing or unwilling" - while the second are under no such compulsion - "may choose to do so of their own accord."
Now, given that, what are the ramifications of ruling that any creature with a name qualifies as a "unique being" and therefore can choose whether or not to enter?
Well, first off, everything has a name, even if you don't know it. So, if I cast the Gate spell and said, "Give me a Balor," then Grim'zk the Undying (an MM standard Balor) might get randomly picked and brought through even against his will, while if I cast the spell asking for Grim'zk the Undying specifically, he'd have a choice.
Personally, I'd say that goes against the entire mythos of calling demons - the better you know your target (like, knowing its name), the easier it is to call.
Also, it doesn't really make sense that a more specifically targeted application of a spell would be weaker than a very specific application.
Second, you've set up an odd situation whereby, so long as I can get a category close enough without naming something specifically, I can pull that something in without problem. Sure, you can't cast the spell, call for Asmodeus specifically, and always expect him to show up, but if I allow the spell to pick "a general of Hell," well then, I figure I've got a 1 / 9 chance of getting him, whether he wants it or not!
No, I think the answer lies in the two groupings: succinctly, "deities and like beings" and "everyone else."
Asmodeus, as a General of Hell, is a "deity or like being." Grim'zk the Undying is powerful, but he's still "everyone else." Even Grim'zk's older brother, Hrazh-kul the We-Aren't-Joking-He-Really-Isn't-Ever-Going-To-Die (an MM standard Balor with 20 levels in Sorceror, 10 in Archmage, and 5 in Weapon Master), though more powerful than his brother, is still "everyone else." At some point, he may cross the line from "everyone else" to "deity or like being," but having a name or class levels *ain't* the spot that marks that line.