Titles usually have a multiple meanings to them.

Heavensward:
1) Reference to Dragoons (Kain in Dissidia shouted Heavensward! when he used his Pride of the Dragoons EX Burst)
2) Flying mounts
3) The Heaven's Ward faction
4) The WoL, having fallen from glory is trying to regain his/her blessing of Hydalyn once more



Shadowbringers might refer to us going to the moon and/or the ascians who are the opposite of the WoL (Which are "light bringers", also the ultimate sword in FFXI was called Lightbringer)