To delete a user account you go to system preferences then users & groups and delte the user from there.
Yes migration assistant will always create a second user using the username that was used on the other mac computer. If by chance you setup your new mac using the same username as the older mac migration assistant will stop and give you a warning that it can't overwrite the current user files (or something like that).
It is up to you to copy and paste your data from that second user account migrations assistant created to your real user account on your new mac. Then you can safely delete that second user.
Or just delete that second account and manually copy and paste from the older mac to the newer one. You would need to network them or use a external hard drive to do that.