To the best of my knowledge, May's maiden name was Reilly and her married name Parker (as Ben was Peter's dad's older brother), and she clearly left it as Parker after Ben passed away. I don't know if she'd change it to Jameson now (I'm just going to pretend that either MA or Ultimate universe are the main canon instead of 616 for the moment, I think, until the Spidey retcon gets retconned and Steve Rogers is brought back to life).