First I think of the Beckhams, as there was a prediction that they were going to use it, then Frank Lampard's daughter, then Luna Lovegood. I think it's one of those names that can come across quite differently depending on surname, sibling names etc. Do you have a middle name chosen? I do like it, btw!
It is indeed Latin, but the ancient Romans didn't normally use it as a name for humans, just for the moon and the moon goddess.
Goddess names (eg Flora, Hebe, Juno) were not really used for people until the Renaissance (15th/16th cent); to take another example, Silvia/Sylvia (goddess of the woods) was introduced to English usage by Shakespeare. Possibly because of the lunatic link, Luna was hardly ever used until the 20th cent.
I love the name Luna, I pleaded to be able to use it for DD but DP vetoed it because it doesn't work well with the surname (I still use it as a nickname though even though her name couldn't be further from it. )