Lyric discussion by reinha28 

Cover art for Sin Nombre lyrics by Refreshments, The

The translation for the song title is "No Name," without a name, nameless.

"Put up wet" refers to riding a horse "hard" to exhaustion and putting him up "wet," rather than brushing him off and cooling him down as should be done.

To me this song is about living a life that you love, in this case that of a cowboy even though it's the hard life. It sounds as if he's being chased in the song, as well, and I would think that he's just longing for an easier, "better" life except the chorus makes me think otherwise. The chorus seems to be alluding to a cowboy who's surrendered his wild and restless heart, and the life so loved by the singer, in favor of the less worthy love of a woman.