Unix-inspired systems have traditionally often had the letter X in their name, e.g.: UNIX itself (ex Unics), Irix, AIX, Minix, NeXTStep, Xenix, HP/UX, Linux, Mac OS X in no particular order.
Of course not all do, e.g. Free/Open/NetBSD (though they were originally based on "BSD UNIX"), Solaris/SunOS, etc.
With that "should end in X" idea in mind, Linus chose to name it Freax (because it was a /free/ UNIX).
When he uploaded a very early version to an FTP server at Helsinki, his friend, who administered the server, changed the directory name from "freax" to "linux", thinking the latter was a much better name. Linus at first thought it would be too egotistical to name it that, but he let the name stick. I'm glad he did.
Of course not all do, e.g. Free/Open/NetBSD (though they were originally based on "BSD UNIX"), Solaris/SunOS, etc.