Migration Assistant multiple use

Your 'get out of jail free' card would be if all you have left to transfer are some simple stand-alone documents, rather than user-specific data, email accounts, browser logins & passwords etc. You could then just network the two together & file-share, rather than migrate.

Each migration will set up a new user account on your new Mac.
Your current stumbling block is you would have to keep generating new names. As soon as you do, it will let you proceed - but don't do that.
Picking this apart manually afterwards is going to be an absolute nightmare.*

Set aside sufficient time to be able to do this in one go & start over. Wipe the Mac & install a fresh new OS. Do the full migration as soon as it asks you, when you're initialising for first use.
You will be considerably better off in the long run.

*Been there, done that, don't ever want to do it again.

The procedure to do a full reset is at Apple KB - What to do before you sell, give away, or trade in your Mac In essence, you want to handle this as though you are going to be the 'next user'.