I know that the phrase cad is aimn duit/dó/di is common in Munster, but I've never heard it used in a plural form. Do these questions look alright?

Cad iad ainmneacha dhaoibh?
Cad iad ainmneacha dhóibh?

Should it be: Cad iad na hainmneacha . . . ?

Or is there some other expression that is more common?

I'd leave ainm singular:

Cad is ainm dóibh?

Answer: X agus Y is ainm dóibh.

^ Same here.

Otherwise, it sounds like you’re asking for several alternative names for each individual person. Could get very confused.

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Not a native speaker.

Always wait for at least three people to agree on a translation, especially if it’s for something permanent.

My translations are usually GU (Ulster Irish), unless CO (Standard Orthography) is requested.

Yes, this makes sense. Irish often uses a singular noun with plural pronouns where there is one object per person.

(I suspected as much in this case, too, but wasn't confident enough to state it outright. Thanks, Scooby and kk for confirming my suspicion. )

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

Sounds like I was making things needlessly complicated.

Go raibh maith agaibh.

You are going to fit in here just fine so!

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