I encountered a lot of problems on my way to transfer from one account to another. At one moment I considered it impossible as the medallion stamp is very expensive / impossible to obtain outside US. So when I tried to transferred the shares I forgot to leave one / some in the old account. I will try this in the future
I know about changing the name or address. But it is not clear what the brokers can use to unDRS. If the key is the account number, then having a new account created with GiveAShare could avoid this situation. Maybe there are other ways to avoid this but I feel that it’s better solution for the moment, as there are so many things not clear