The right time to transfer information is when you initially set up a new Mac because Migration Assistant will always create a new User Account.
You can rename the originally created User Account to some arbitrary name, then log into that Account and rename the one you want to use. Then, log out of that one, log into the other one, and erase the originally created User Account.
For details refer to Change the name of your macOS user account and home folder - Apple Support and Delete a user or group on Mac - Apple Support respectively. The reason for changing the originally created User Account first is that it probably bears a name you will want to use.
If that sounds too confusing just erase the Mac and start over: Erase and reinstall macOS - Apple Support. This time, when asked if you want to transfer information from another Mac or a PC, choose that option.
Refer to Move your data from a Windows PC to a Mac - Apple Support.