Welcome to Wikitree Kathleen :)
It is definitely ok to use your surname, in fact by doing that, it makes finding new "cousins" so much easier. It also goes a long way to being accepted on a trusted list if you ever need to be put on one. People like to know who they are adding :)
There are also a number of privacy levels you can choose for your profile. Just click the padlock top right on your profile for the different choices and explanations :)
I hope you enjoy Wikitree as much as I do. :)