"can someone please explain to me the meaning behind the name "catch as catch can"?"
I believe the US version of 'Catch Wrestling', was mostly influenced by the Lancashire (an English county) style of folk wrestling.
Obviously the aim is to try and 'catch' your opponent in a hold hence the phrase "catch'us, Catch can", which in the dialect of the area (and if said with the correct accent) mean 'catch me if you can'.
I think as the style moved across the Atlantic, Lancashire Wrestling basically became known by this phrase, which became 'catch-as-catch can' and eventually just 'catch' as Lancashire dialect was lost in translation.
Somebody please feel free to correct me if I am wrong.