Not clear to me. One presumes that one would need distinguishing parameters of some sort or you could end up with the wrong person.
However, if the demon is initially bound by a name and one does demon summoning rituals (even if the demon isn’t summoned to you) the true name used in the initial binding works as expected with no additional parameters being needed.
Now, what happens when you attempt to bind a new demon for the first time and their name is already taken?
you can’t have 2 demons in the abyss with the same true name. That we know. Does the binding/incarnation then fail? Or do other parameters get bound into the name.
If I were to guess, for lesser wizards it would fail, for greater wizards with really powerful spells, they can probably work something out that alters the name enough to force the binding. Remember, spelling is also important and this presumably has some leeway given different alphabets/runes etc.