Does a pilot have to request altitude changes when receiving flight following?
No, you wouldn't need to advise of changes if all that they instruct is "maintain VFR."


  91.123(b): "... no person may operate an aircraft contrary to an ATC instruction in an area in which air traffic control is exercised."


It would depend on the instruction received.  Let's say, after departing from class 'C' airspace, they told the pilot, "maintain VFR and resume own navigation," they are giving him freedom to choose his own headings and altitudes.

On the other hand, if the controller said, "maintain 5,500 and turn heading 030," then the pilot would need to cancel flight following or make a request to change instructions.

Bottom line: don't not do something they do tell you to do.