As a rule, GAR posts could only be named after someone if they were deceased. I suspect that, perhaps, this one is named for a lad named
Samuel Trescott (1842 - 1864) who died in Andersonville Prison. He was a member of Company C, 2nd Ohio Cavalry.
As I was writing this
@Library Lady beat me to the find a grave link.
The post was originally formed in 1866 as Trescott Post #10 - One of the very post post in the GAR. They disbanded and/or reorganized by May 1869 as Trescott Post #84
Almost certain that it is named for Samuel Trescott - unless some other Trescotts in the county or area died
before the post was formed in 1866