It sounds like that previous owner did not properly remove their Apple ID and prepare this Mac BEFORE they sold it. Changing the device's Administrator name and/or password may not be all you will need to do to be able to keep it updated going forward.
Regardless, I am assuming that you can log into this notebook with an administrator-level account correct? If so, you can easily create a second administrator account with the name you prefer. You can then, log out, and then, log back in with the new administrator account. If all works as you expected, you can then delete the other administrator account.