How can I create a hard link to a file, then rename the hard link to a different name?
man ln
ln <original_file> <link_name>
Renaming would be usual renaming. No special stuffs required.
Btw, Why would you want to rename? use the final name while creating link?
EDIT
From your other post in this thread, Renaming wont change the inode of the file.
Please let us know what you are trying to achieve.
Or, if you are renaming a file without moving it across a filesystem boundary,
mv oldname newname
will rename the file without changing the i-node number.