Found a solution in the "More like this" sidebar. First, logon to www.iCloud.com and open the Mail window in the iCould window. At the upper right (I think) is a gear icon, which gets you to preferences. (My iCloud account had my name right.) In the Mail preferences there, change "Full Name" to the correct name.
It may take a few minutes for the Mail program to catch up to the change. I quit Mail and then restarted it. Then checked Mail>Preferences>Accounts and it had my correct name. Then start a new Mail message and go to the pulldown menu for From, and select your correct "From".
I had an additional problem in that my Contacts had my husband identified as "Me". Had to delete that card, then select my card and from the "Card" pulldown, select "Make this my card". Then reenter my husband's data on another card. Safari's Autofill draws info from the "Me" card in Contacts, so if this is wrong, you will want to fix it too.