Migration assistant

"migration assistant which wants to create a new user on the new mac "

That's because you're using the same user name on your new Mac. Migration Assistant will transfer your old user name to a new Mac. If you created a user with same name as on your old Mac, you will be prompted to create a new user name.

When you first turned on your new Mac, you should have used Setup Assistant to transfer all of your user settings to the new Mac. If you skip that, then created a user name identical to the one used on your old Mac and then used Migration Assistant, you'd have arrived at your current situation.

There are a number of ways to fix this:

1. Start over with your new Mac by erasing the drive reinstalling the OS and then use Setup Assistant to transfer your old user account to the new Mac.
2. Create a new admin user with a temporary name on your new Mac, switch to that temp user account and sign-out of the previous one, then delete that user account that is the same name as used on your old Mac. Then use migration assistant to bring over your old account from the old Mac.
3. Perhaps the easiest of all, just copy your photo library from the Users/Pictures folder of your old Mac to the same location on your new Mac. Then configure your Photos application to use that library. By the way, you didn't indicate which photos app that you were using, i.e., Photos, iPhoto, Aperture, etc.

Perhaps someone else can chime in about being able to do it with TimeMachine.

I don't use TimeMachine personally, and am just not that familiar with using it. I prefer using Carbon Copy Cloner for backup proposes, and have just never found a need for TimeMachine.

Do you still have your old Mac? Copy the "Photos Library" file to an external drive, then copy it to the same location on the new Mac.