expressed desire to add a nice custom watch to their collection
Well, DeAnna, what does that mean? To have a truly custom made watch
that can be produced economically requires a watch factory. To have a
mechanical watch, as opposed to a case for a quartz movement,
requires an even bigger factory. In those cases, talk to Seiko, Rolex
or Patek Phillipe.
I suspect that what you really want is a promotional watch of some
sort, which is far easier.
A Google of “custom watch design” brought up many - here’s a couple: