Normally I won't expect any problems as it will be the same domain.
All user-guids stay the same and a connection between domain-users on the SQL instance can be paired again.
Due to the login process onto a SQL Server, there is no key or a checksum changing, so just remove the server from the domain and rejoin.
Maybe you should check if the SPNs are still exist => better you have a list of al required (or actually created SPNs) for that SQL Server that you'll be able to re-create them.
https://www.mssqltips.com/sqlservertip/4875/script-to-check-and-auto-generate-spns-for-sql-server/
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