Answer:
"Morgan" isn't something like "kleenex" or "scotch tape" that once referred to a specific product. It describes a specific type of silver dollar, and is named for the artist George T. Morgan. Morgans were struck from 1878 to 1904 and again in 1921, so you could not have a 1923 Morgan dollar. All dollars struck that year are Peace dollars, again named for their design.