Issue with Delete & Create Same Login Account For Read-Only Access in SQL Server

I was trying to create a user that has Read-only access to one database. Had issues with this user not able to access the database. So I started to delete the Login Account and recreate it again and that where I started seeing the issue. I was able to create another user account with RO right with no problem. Unfortunately, we have other supporting staff needs the same login name. So I am stuck with the name. So how to make sure the login account is completely removed and is not being locked by any resources so when I create it again and assign the Read access it won't be any issue??