I just happened across a New Zealand band called "The Phoenix Foundation" and apparently they got the name from MacGyver.

It seems they liked the show as kids.

Heres an excerpt from the blog entry which has an interview with the singer Sam Scott (SS)

-- snip --
DL: Speaking of your name, I'm interested in hearing about the origin of the band name, knowing that there's a couple interesting possibilities.

SS: It was from the television show MacGyver [the corporation that Richard Dean Anderson's character worked for] but also kind of making joke of DJ groups in Wellington who had names like the Roots Foundation... Dub Foundation and names like that. It's sort of a silly name in light of that, but here it is nearly ten years later and we can't change it now. But MacGyver was a cool show when we were kids so...

-- ends --

Further in the interview they mentioned the political Phoenix Foundation. I wonder why the MacGyver writers chose that name since there already was a Phoenix Foundation. Anyone know?

Because it sounded cool.

was it around when they wrote the show?

Aye.
According to this anyway.
http://en.wikipedia.org/wiki/Phoenix_foundation

They're not an actual organization.. they just a bunch of trouble making hoods, who haven't been heard from since 1980.

Can't see any real reason for the writers to reconsider the name because of a bunch of failed wannabe libertarians

Speaking of bands inspired by MacGyver, I have run across a few bands with names from the show.
I've seen one named Murdoc, one called MacGyver's Dog- and one actually called MacGyver.