There is no real necessity for 'getters' and 'setters' to have the same name as the internal field. In fact many would argue that linking the two together is a violation of the data hiding principles of object oriented programming. Part of the point of having getters and setters is to protect the rest of the code from changes that are internal to the class, like renaming.
Having said that, if you absolutely decide that you need to rename the methods as well as the fields, then Eclipse will do it for you. You have to do them separately, but the same 'rename' that you are using for renaming fields works for methods. Just select the method and do what you did before.