Before a verb, an is an interrogative particle.
Before a noun, an is the singular definite article. Aontas is a noun.
A "basic sentence" in Irish is "verb subject object", and putting an before the verb turns the sentence into a question - but this isn't a full sentence, because there isn't a verb in it, so the only thing that makes it a question is the question mark.
"Aontas" is a masculine noun meaning "union". When preceded by the singular definite article "an", masculine nouns which start with vowels are given the t-prothesis:
For capitalisation, we remove the hyphen and capitalise the noun itself so you can easily tell what the word is.
An Taontas Eorpach
An tAontas Eorpach
The latter makes it clear that the word is "aontas" and not "taontas".