migrating data to new mac

If it were me, I'd simply erase the Mac and follow the procedure here: What to do before you sell, give away, trade in, or recycle your Mac - Apple Support

Doing it this way ensures there's nothing left behind from the previous owner.

Then I'd examine the possible ways of migrating:

• Via Time Machine Backup external drive. Back up your old Mac to your Time Machine backup, then connect it to your new(ish) Mac and go thru the Setup Assistant. (Note that the password you'll be asked for on your new(ish) Mac can be the same as your old one...it doesn't need to be different. The key here is to write down your password, as resetting a "forgotten" password can be time consuming). I'd recommend this method to most folks.
• Via Ethernet cable. You can connect both Macs together (although you may need one or two adaptors) and go thru the Setup Assistant.
• Via WiFi (as long as both Macs are connected to the same WiFi). I don't recommend this method, as it's too susceptible to signal dropouts and, thus, corrupted files. Use at your own risk.

You COULD check the user account the previous owner created and ensure it's an Administrator account. (Users & Groups). I'm assuming the previous owner provided the new(ish) Mac's login password? If you know the login password you can create a new user account (ensure it's an Admin account), then delete the one created by the previous owner. (Renaming an account isn't as easy as you'd think, and it has created issues for some when they didn't precisely follow the renaming procedure. That's why I recommend starting with a blank slate).

Hope this helps.