When did they change the nomenclature from "Ball & Co." to "Ball Watch Co."?

The name change occurred in the early years of the 20th century. There's no hard and fast date because of the time needed to use up stocks of the Ball & Co.-marked components, which varied from model to model. Remember, they never threw any usable parts away.

I think it's safe to say the transition was complete by 1906.

I think the first Hamilton Ball 18sz Ball Watch Co mvmt was 90751. It was a commercial standard model. The first Hamilton Ball Watch Co ORRS was 118551.

Discussions and theories about transition times usually involve dials.

happy hunting