Madmartigan is a rock band from Austin, Texas.
While I have not seen any evidence that the name is a reference to Willow, some of their song titles ("Waltz of the Chupacabra", "Riding Dragons...") at least make it seem possible based on an interest in fantasy.
The construction of the titles makes it seem like they aren't taking anything too seriously, and band photos show them having a good time. The overriding feeling of the music is a bit more serious. There is a plaintive quality to the delivery, and it is reflected in the lyrics. "Paper Thin" is a good example:
You are a tornado and I am just...
Feeling kinda paper thin, falling over through the wind.
It may be that the obstacles that they see in the world appear to call for mythic heroes, and they don't feel that is what they are bringing to the fight. If so, that's okay; lots of people have that concern, and it can help to have it put into song.