Hello - I stumbled upon your post while researching a person in my family line and who lived in Perkinstown.
So far, I haven't found info on the naming of Perkinstown online.
In case you haven't learned the information you seek, as a former public library reference librarian with experience of answering such questions for the locality in which I worked, I'd recommendyou may wish to telephone one of the places listed below and ask if they have info on the origins of the place name Perkinstown.
Frances L. Simek Memorial Library (public library) 400 North Main Street Medford, Wis. 54451 715-748-2505 (Medford is the county seat) For library hours: http://www.sws-wis.com/medfordpubliclibrary/http://www.sws-wis.com/medfordpubliclibrary/
Taylor County Historical Society 224 S 2nd St Medford, Wis. 54451 Phone: 715-748-5163 I couldn't find a web address for the Historical Society for info on their hours.
I'd telephone the public library 1st.If they don't have the info, they will probably refer you to the Historical Society and can give you the hours someone would be there to take your call.