You don't have 2 "programs" ... you have 2 "logins" as shown.
You must have gone completely through the initial setup on your new Mac and
then used Migration Assistant to move your old machine over to the new one (rather than doing the migration as part of the startup routine prior to creating your user account). Thus, you have the new Mac initial login account (Lewis Knudsen), and the migrated account (Lewis Knudsen 1). Since you probably didn't do much after creating the new Mac account, you probably want your original login from the old computer.
If you login to the "
Lewis Knudsen 1" account, you should see your old desktop, apps, and data from the old computer. You can then go to "
SystemPreferences / Users & Groups" and delete the "
Lewis Knudsen" account. Simply unlock the padlock at the bottom, select the account to delete, and press the "
-" button. You can totally delete the account when asked.
That's it...