Effect of PhD advisor name/department on my future
For most people, any such effect is very short lived. It can help you obtain your first job, of course. But after that your reputation is your own and after a while, no one will remember or care who you worked with prior to earning your doctorate. 

There are exceptions, however. Some, usually prominent, people maintain long term relationships with their former students and write co-authored papers. They might also have an active visitation program in which people visit one another's institutions to work on things or just give seminars. In a situation like this, it is the group founded by the professor that helps you build your reputation and keeps you connected to the larger work of the group. In such a situation your relationship with the professor moves from student to colleague and can be mutually reinforcing. Working initially with such a person can have long term effects, of course.