I am not too sure, as I have never done this before. on the face of it, we can give the standard answer: It depends. How is the partner server defined in your mirroring setup?
Most likely, it is defined by server DNS name. If this is the case, you could put a host file entry on each machine, pointing to the old name. This will get very dicey, if you ever re-use the old server names.
If it is by IP address (not really a best practice), then there is likely no change necessary.
In the case, where you have a smaller database to test with (may as well set up a dummy database for this), see if you can issue an ALTER DATABASE statement to change the partner name. This will require a host file entry, so the system can resolve the new (fake) name.
Worst case, you will have to rebuild the mirrors.