Some cowboys mistakenly use the term houlihan (hoolihan) in place of hooley-ann, the head catch with a loop. Some spell it hoolihan and pronounce it hooley-ann.
Adams, "Western Words" (1936), and Hendrix in his "Roping" (1935), as previously noted, properly define hooley-ann.

The name hooleyann, some Texans claim, may come from the town Hooleyan (formerly Hooleyann), Texas, which was founded in the 1890s. It is four miles south of the Red River in extreme northwest Hardeman County, northwest Texas. The County was covered with prairie, and the western half is still ranching country. See the Handbook of Texas, on line: Hardeman County

There's a bit of western poetry somewhere on the web that has this verse. I just have a piece of it; if I find it again I will give the website:

'Cause he'd duck an' dodge an' roll back on his hocks like Peppy San,
While I'm snaggin' air an' fence posts with my handy hooleyann,
An' if by chance he tripped my snare, he'd rear an' pitch an' paw,
An' leave me plowin' furrows with my nose an' bottom jaw.