I like @TomCotton's suggestion, but I thought I would add to it by providing some other options in Smith's Copious and Critical English-Latin Dictionary.
I think, first of all, that quaestio is not a good translation of English question. If you look through the Lewis & Short entry for quaestio, the word has a technical legal meaning and is also used to refer to something closer to the English word investigation. The Scholastics would refer to different topics of investigation, such as Utrum Deus Sit, as a quaestio, but I do not think they would regard Quid tibi nomen est? as one.
That said, Smith recommends rogatum or interrogatum as a more direct translation.
To answer a question would thus be ad rogatum respondere, which has good classical precedent:
Cicero uses this construction to refer to rhetorical questions in his Orator:
sic igitur dicet ille, quem expetimus, ut...interrogando urgeat; ut rursus quasi ad interrogata sibi ipse respondeat. (Cic. Or 40)
Other examples substitute rogatum with another word:
ad ea, quae quaesita erant, respondebat. (Cic. Phil. 1.1)
The ad appears to be unnecessary, at least in colloquial speech. Here is Plautus:
hoc quod te rogo responde mihi. (Pl. Merc. 1.101)
etiam tu hoc respondes? (Ter. Andr. 2.2.8)