Woodcock is a fairly common American and English name, same as the bird. I went to school with a kid named Richie Woodcock, not to say he didn't collect plenty of shit all through high school.
A more relevant question, I think, is how did Shemp end up doing shorts for Columbia at this particular time? Did someone detect Curly's health failing and bring in Shemp for a few dry runs? This is apparently what happened in some live appearance tours, which were Moe's department, not Columbia's, could Moe have been working behind the scenes at the studio as well? Shemp was a freelancer all over town to this point, and had rarely had this much concentrated exposure before, at Columbia or anywhere else. I don't think it was because Columbia was specifically looking to replace Charley Chase, he was long gone...I'm more inclined to think they recycled the Chase shorts to break in Shemp, which, if true, shows very sly long-range thinking by Moe, who, in his book, claims to have fought hard to get Shemp as Curly's replacement. Maybe harder than has been realized.