MY MAILS SHOW A DIFFERENT NAME, THERE MUST BE A PROBLEM WITH MY APPLE ID, WHAT CAN I DO?

YEARS AGO MY WIFE CREATED AN APPLE ID WITH MY EMAIL, THEN SHE CHANGED IT TO HER OWN EMAIL AND FORGOT ABOUT THIS ONE. I JUST BOUGHT A MAC AND WHEN I INPUT MY EMAIL IT TOOK THE OLD NAME OF MY WIFE`S ACCOUNT. NOW WHEN I OPEN MY COMPUTER THAT OLD NAME APPEARS AND IT ALSO SHOWS IN ALL THE MAILS I SEND (FROM THIS COMPUTER). I HAVE CHANGED MY NAME IN "www.myappleid.com", BUT THE NAME HASN`T CHANGED. WHAT CAN I DO?