We know a little girl called Etta (she's about 10 I think) - I think it's lovely on its own. Don't agree with a longer name 'just because'. We have a Max, because we liked it and I didn't like any of the longer versions (too posh, too American, too Gladiator etc etc).
If there's a longer name you actually want to call her, do it. I find a lot of names ending with '-etta' are far to frilly, personally. But if you just want an "Etta", don't artificially call her something longer.