Other answers say it all, but I will just add a personal experience.
My name is Mohammed Halabi, do you know how many variations my name's spelling has?
Mohamed
Mohammad
Mohamad
Muhammed
Muhammad
Muhamad
Muhamed
Same with my last name, it can be Halabi or Halaby or even Halabe!
Basically, every boarding pass I ever had was with a different spelling, and I never had any problem. In your case spelling is right, no one will notice. Just enjoy your flight with your girlfriend Jones ;)