What does your name mean?

[Rase]

Ryan mean "little king" or "little ruler". It's Irish. I am not.

The Irish for king is "Rí", pronounced Ree. Dunno what the "an" is for, though.

Well, according to the site Yu-Yevon linked to:

From an Irish surname which was derived from Ó Riain meaning "descendent of Rian". The given name Rian probably means "little king" (from Irish rí "king" combined with a diminutive suffix).

So I would assume the "-an" is the diminutive suffix, similar to "-ito" or "-ita" in Spanish. Basically it makes whatever the thing it's attached to "small" or "little".