Renaming "A's MacBook" to "C's MacBook" I see that my Mac is called "A's MacBook" on the network.

How do I rename it (i.e., change the hostname) to "C's MacBook"?

That's the question. Here are the details:

Having read various suggestions to create a superfluous admin account before migrating using Time Machine, I went ahead and used "A Admin". The trouble is that that resulted in the hard disk getting named "A's MacBook", which does not match the directory under /Backups.backupdb on the Time Machine disk.
One can rename one's "Computer Name" under Sharing in System Preferences.