As in, the common Spanish feminine name. I always assumed it was -a (because of Spanish language gender rules), but I ran across it online in a few places as being -o. Is -o correct? Or are both in use?
Both. The name was originally Consuelo, which means “consolation” or “I comfort”. Consuela is derived from that. There are other Spanish female names that end in -o – the one I can think of most easily is Rosario, which means “rosary”.
[QUOTE=Bambi Hassenpfeffer]
Both. The name was originally Consuelo.
[QUOTE]
Which, coincidentally is the answer to the question “What do you call a Mexican woman with no legs?”
That’s terrible! 
Another is Rocio (for a long time I thought her name must be Rocia, but it isn’t, at least in the case of our neighbor).
And Rocío means “dew”. The common thread through all of these is that the names are nouns, not adjectives. Since they aren’t adjectives, their endings won’t necessarily match the gender of the person or object they’re attached to. Many nouns (occupations, mostly) have feminine and masculine forms, but not nouns like “comfort”, “dew”, and “rosary”, because these are objects, not people.
Another Spanish girls’ name ending in ‘o’ is Amparo, which means ‘shelter’.
Then you have the masculine nouns ending with ‘a’, like ‘problema’ and ‘tema’ - I read somewhere that this is when the word is of Greek, as opposed to Latin, origin.