The Naming of Williamstown
The first settlement in the area was Littell's Station, after James Littell (1754-1833), whose son William (1789-1823) was an early advocate of the creation of Grant as its own county. (You can read that Grant Co. was so-named because of William Littell's insistence to the legislature that they “grant” the creation of his county. That's just wrong). Littell's station was on the north branch of Fork Lick Creek
Multiple sources say as early as 1809, there was a post office, called Arnold's, on the location that is now Williamstown. On the other hand, USPO records have no such listing. In any event, a post office of the time would have been a cigar box in the corner of a small store - not a huge operation. The location was the site of the farm of William Arnold (c.1750-1836). Arnold donated land for the court house and other public buildings when Grant County was created out of Pendleton County. His doing so pretty much assured that the local area, now the county seat, would grow and prosper.
So folks decided the new county seat needed a name. They decreed it to be “Philladelphia.” That's not a typo - it had two l's in their proposal. The name lasted for less than a month, when it was discovered there was already a town of that name in Kentucky. We find numerous locations for a "Philadelphia Church" in Kentucky, but the location of the other Philadelphia appears lost in history.
The name Williamstown was established as a post office in 1822. The explanation commonly given is that it is named for William Arnold, but there's no reason it couldn't have been for William Littell, or both.