SYMPTOM:
The option to rename Partition Mapping Tables is grayed out, as shown in the screenshot below:

CAUSE:
This is a known issue in Strategy Desktop 9.x which is being investigated.
ACTION:
This behaviour has been corrected in Strategy Developer 10.x. To take advantage of this fix, please upgrade.
WORKAROUND:
The Partition Mapping Table name can be renamed by running the following Command Manager outline:
ALTER TABLE 'current table name' NAME 'new table name' FOR PROJECT 'Project Name';