What Apple device? If on a Mac, in the Mail menubar click the Window menu and select "Previous Recipients":

Scroll the resulting list for your old name and, if you find it, delete it.
I cannot find Apple instructions for this on an iPhone or iPad. A web search for "clear recent mail recipients on iPhone" picks uip some non-Apple instructions.
First, make sure your old name does not still exist in Contacts. You may find it from starting a new email message on your phone. I found a listing for my old e-mail address that's been dark for 4 years by entering my last name in the "to:" field in iPhone Mail.

Clicking the "circle-i" info icon for that entry took me to a Contacts card with the out-of serice address which I zapped.. Might work for your name as well.