What is the name of the 'Halo 3 theme song'?

What you've linked to is actually the Mjolnir Mix featured in Halo 2. It is a remix of the original Halo theme, from Halo 1.

In Halo 3, there are a few songs you could potentially consider "theme songs". They are Never Forget, Finish the Fight, and arguably Behold a Pale Horse, which contains samplings from many other songs in the series. A remix of the original theme is also used and it is One Final Effort. A slightly different version of this can be heard in the Warthog section of the last level.

My OCD got the better of me, and I had to check. In the level in Halo 3 where you drive the warthog through hell to safety, the song actually playing is "Halo" (the basic theme). See wikipedia entry on the soundtrack. The version in the video above is the "Halo Theme Mjolnir Mix".

As a bonus piece of trivia, it is actually available as a downloadable track for Guitar Hero 3. If you are a fan of the game, it feels pretty sweet to rock out to it on the plastic guitar.