Facebook is implementing so many security methods to prevent spam. When you create a page then there are certain limitation also. Even you cannot change you Facebook name after a certain limit is reached.
Yesterday i tried to change a Facebook page name then i faced problems again and again. I observed it and i understood about it.
As i observed, there can be three problems if you are unable to change you Facebook page name.

100+ Likes

Yes, if your page has more then 100 likes the you cannot change your Facebook page name. Be little tricky and careful about your page name. So you don't have to change it again and again :)

Using Facebook as...

You cannot change page name if you are using Facebook as page name. Switch back to your account then try it, or it may redirect you to an empty page every time. :)

Using Symbols

You cannot use symbols in Facebook page name unless you use some sort of softwares. :)

Name Length exceeded

If you use a long name then Facebook will not accept it. There is a certain limit of Facebook page names.

Name changed again and again

Don't irritate Facebook by changing page name again and again. Facebook will allow you to do this.

Few other reasons can be...
Your internet connection is not working.
You didn't clicked properly.
Your computer is hanged.
You Browser stucked.
You have a slow network. :D

Just kidding, enjoy and Hit Like. :)