So, as I said before, I have no experience with birth. So that's that. Now. About the whole, Female = Luna thing.

Yes, turned females always become Lunas (not Wren). But werewolves by birth (like Keira) are born with ranks. Most of the time, they are Omegas. But the occasional powerful born were-woman can be a Gamma or a Beta. Not fair, but that's how it works. If you were confused. 

Also, June is a Beta. You can tell this because she was born a werewolf cub. Born female wolves who shift before their 3rd birthday are always Betas. Also, Jude was a Beta, so you know, Beta blood and all that XD