Network Printer

I have a network printer that keeps changing it’s name each time the client logs on to their PC, and when another client needs to print to it, we need to make the changes to the printer name on the machine that needs to print to it. This is on terminal server, and the actual printer name doesn’t change, but the session that the client logs in does. How can I stop this from changing each time the client that has the printer connected to their PC logs on?