How do I rename a book mark on my iphone?

Tap on, and hold the tap, until you see various options, one of which is "Edit:"

What happens after you "tap and hold?" In order to see the entire display be sure to "scroll up."

You have to be viewing the Bookmarks screen. Click on the Bookmarks Icon at the bottom of your screen to view a list of your Bookmarks:

You are welcome.