Why must we know that he “has a name…that no one knows but himself”?

The term name can refer to the term commonly used to summon a person. The word name can also refer to one’s reputation and so express the essence of your character. The first possibility is excluded by the fact that the name of this rider is revealed to us in Revelation 19:13 and another name given in Revelation 19:16. The second possibility recognizes that a reputation is built, and revealed, over time. The rider went out conquering and to conquer (Revelation 6:2), but what you set out to do may be a different thing than what you end up achieving. This rider has already achieved many victories (witness the crowns), but his work is not yet complete and so his final reputation not yet publicly cast in stone (though the final outcome is certainly known to him; hence the words no one knows but himself).