May is named after Maia, the goddess who oversees the growth of plants.
Compare what Ovid wrote about the name of May:
> You may ask whence I suppose the name of the month of May to be derived. The reason is not quite clearly known to me [because there are too many theories].
[J. G. Frazer's translation for the Loeb series]
That the name honors a Maia is one of three theories he goes on to present, the others being that May is named after the personification of Majesty [maiestas] and that May is named in honor of society's elders [maiores].
For April, on the other hand: classical Latin Aprīlis, use as noun (short for mēnsis Aprīlis month of April) of masculine of Aprīlis of April, of uncertain origin; perhaps < Etruscan.
(Oxford English Dictionary is a great resource. In the UK you can often get free online access through free membership of a public library.)
Absolutely true, but difficult to get access from the US without a university affiliation.
However, it isn't obvious that the OED is a better source on the meaning of a classical Latin month name than a classical Roman is. It's certainly possible, but not close to a slam dunk. And the OED is appropriately hesitant to say that it knows the origin of the name.
I'd be curious when the entry was updated, except that I can imagine the entry for "May" being updated for quite a few other reasons than to review the etymology.
(I might as well note that Ovid also presents two theories for the name of June, one that it is named in honor of Juno and one that it is named in honor of either the goddess Youth [Iuventas] or youths [iuvenes] in general, forming a contrast with May. There appears to be no real distinction between honoring Youth or honoring youths, despite the fact that honoring Maiestas and honoring the maiores are explicitly presented as separate theories.
I would say the June-from-Juno theory is on much stronger ground than the May-from-Maia theory simply because Juno is so much more important a god, but that is also open to debate.)
Curiosity should be rewarded!
"This entry has been updated (OED Third Edition, March 2001; most recently modified version published online September 2022)."
And there's a link to "Previous version: OED2 (1989)" where the etymology is given as: ... "The etymology of the Latin name is obscure; some ancient writers connected it with the name of the goddess Maia."
(Since you read Ovid probably there's nothing new for you in that!)
January, March, and June are named for Janus, Mars, and Juno. February, April, and May are not known to be named for any god, nor is there any particular reason to believe they are.