You need to have your e-mail verified and volunteer to help the WikiTree before you can do too much, though if it's your own profile you may be able to edit it; I forget the details, but to do much you need to also sign the Honor Code. Then you'll be a Wiki Genealogist and can edit most things. On each profile that is open to being edited there is a edit tab at the top and also one toward the bottom of the biography portion of the profile. If you want to modify the last name you will end up changing the ID number of the profile as an ID consists of the surname and a sequential number for that surname.
Warning, there's a bit of a learning curve on WikiTree, so don't get frustated if you don't get things right at first.Just keep asking questions and trying things. And take time and read as much of the Help Files as you have time for as they will answer lots of questions before you find you need to ask them.