These are items called "titles" and you can apply them as often as you like. (If your LI has one, applying a new one will overwrite the old.) They are available from epic quests (one-time quest rewards), repeatable quests (once-per-day rewards), skirmish camp, and various reputation barterers; some basic LI titles are also purchasable in the store with TP. The basic titles from skirmish camp and the in-game store are not worthwhile, for the most part, so save your TP and marks for other uses.
Originally Posted by Adam_M_14
Most players I know pick one LI title and use that, and would only apply a new one if they decided to alter their build. You could change your LI's titles frequently, and this could be done inexpensively if you only used titles from the repeatable quests, but I think that's a fair bit of wasted effort. It seems even more wasteful to do that with reputation-barterable titles.
See Legendary Titles on lotro-wiki for a listing of the various titles in the game.
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