Do I have two male anoles?

My husband caught two anoles and I think they are both male, even though we gave them male and female names.
They both have dewlaps, but I did hear that females can have them too.
Plus, I saw them fighting(?) one day. The supposed male was on top of the supposed female and biting his/her head. Plus, the supposed female hides all the time.
We have a 10 gallon tank for them - if they're both male, do you think they'll be okay?
Well without a pix I'm just guessing at your question but i have a hundred anoles in my yard here in Florida and the males are much larger and have a crest that they can raise up running the length of their bodies. The have a large red or orange dewlap and slight bulges under the tail. The hemi-penises. Females are usually patterned with either a light colored stripe or a whitish diamond pattern down the back. Small dewlap and no tail bulge. If she is gravid with eggs she may be hiding from the male and he may be trying to mate with her. Males mate by grasping the female by the back of the neck while wrapping their tails under the female. Usually once the female submits he will release her neck.
Male will fight by puffin up and trying to make themselves look bigger. They do get into real knock down battles with each other.
Make sure they have plenty of places to hide from each other and if the fighting continues release the lose or it will die.
If they are a pair offer them a potted plant to lay eggs in.
Keep the agressive one. Get rid of the passive one.
The tank is not big enough for both of them.
Male Anoles will not be ok together. The stronger one wiill keep the weaker from eating and starve it to death. It maybe ok in a larger tank, like a 20g

You do have 2 males, not a female and male.
Well, looking at the behavior that isn't there, you either had two males, or a male and a female that don't get along.
Usually if theres a male and a female, the male will do a display for her (it looks a bit like push ups and then he'll puff out his dewlap). I can't remeber if the females have dewlaps also, but I don't recall mine ever flaring up - I only remember the male doing it. If your tank is big enough and your lizards still arn't getting along, I think its possible to get a divider for the tank so they'll each have their own territory.Oh, and just a tip - if you have lizards, don't keep cats. I speak from experience!
A 20 gallon would be a better size, for more than one.

If the anoles are adults, the females will have a light stripe down the back while the males doesn't. A male will have a large dewlap and display it more often.
Females have very small dewlaps. To tell whether you've got males or females, just pull on their throat skin. If you get a full dewlap to come out, it's a male. If you just get this little tiny nub of a dewlap, it's a female.
Males have a colored throat flap and females do not.
Carolina Anoles are red and Bahamian Anoles are blue.

Male Anole:

Female Anole:

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