Why would the old players not get the right name plates?
Assuming the property is properly replicated, and there is appropriate data binding from the property to the name plate, it should Just Work ™ when you change the property on the server.
In fact, if you read the property value from the player to the GUI using property binding, you don’t even need RepNotify, just regular replication. Just update the property value on the server, and it replicates out to each client, and they all draw the right value.