SSL Certificates - Terminal Servers - Swapping - Annoying Warning Screen

I have 2 terminal servers.    One in production, and a brand new 2nd which is now ready to replace the 1st.   We have two SSL certificates (from godaddy), one on each machine, named TS.ourdomain.com and TS2.ourdomain.com, where TS2 is the new box, both match the A records by the same name to point to the actual server IPs.   We installed thse certificates under the TS servers RDP-Tcp configuration screens. So far so good.  

For our remote users, they only know the TS.ourdomain.com name, we don't want to have to tell'em to switch to a new name.      

We just swapped new TS2 to replace TS.   This is easy to do by simply going to Godaddy and swapping the A records for TS.ourdomain.com and TS2 box.   Now  TS.ourdomain.com points to TS2 box IP.  Aok.  

Problem:  Everything works fine for our users, but they now get an extra annoying Certificate Warning/Error about the name mismatch.  In their RDC Desktop, the server name they use is still TS.ourdomain.com, but the SSL certificated installed in the new TS2  is named TS2.ourdomain.com.

Question:  What's the easist way to fix the certificates?    Is there an easy way to swap the certificates?    Or maybe somehow alais the SSL Certifcate on the new TS2 to repond positively to clients coming in TS.ourdomain.com?   Or do I have to back to the painful process on GoDaddy and redo the certificates from scratch?