According to "The Wild Wild West Revisited", James West retired at some point in the 1870's and moved to Mexico, where he fathered several children by different mothers. West may have been following a family tradition - it could be that his own grandfather sowed a lot of seeds across the West. That is, if his grandfather can be definitively locked down as Pasquinel, a fur trapper who worked in the region now known as 'Centennial', Colorado.
Noted Wold Newton researcher Dennis E. Power posits that one of James West's sons was the father of famed 60's private eye 'Honey West'. (Personally, I'd tack on another generation between James and Honey.)
I think there were enough West children that many TV characters can trace their lineage back to James T. West. And not all of them need to be named "West". At some point one of his children must have moved to Hawaii and that's where we'd find grandson Tommy Lopaka (as seen in 'Hawaiian Eye'). Another grandson kept in the family business - Thomas Remington Sloane III, a spy for UNIT. As he needed to protect his identity and for the safety of his family, the surname of Sloane was an alias. The "III" was meant to disguise his family connections three generations back so other members of the West family couldn't be tracked down and used against him. (His adventures were chronicled in 'A Man Called Sloane'.)
Another who joined the spy biz - albeit reluctantly - was Jake Webster. Again, he was probably using an alias when he was running a nightclub in Vienna, where he was conscripted by the government into acting as their agent. The government probably stumbled on him as a candidate as there was another Jake Webster on their books, working the same kind of deal in Munich. (The Vienna Jake Webster was seen in the TV series 'Assignment: Vienna'. The other Jake Webster was introduced first in the TV movie/pilot "Assignment: Munich".)
Moving ahead yet another generation, we have someone who still bears the family name of West, but he and his immediate family have wound up on the wrong side of the Law. (Being the good guy isn't genetic. Just ask James West's grandson Milo Janus, as seen in 'Columbo'......)
Wolfgang West is the patriarch of a family of con men, thieves, and fences and he is now serving a five year sentence in prison. The story of his family has just begun in the new series 'Scoundrels' and like the characters in 'Ugly Betty' and 'The Office', many of their personal details can be found mirrored in a similar family elsewhere in the world - the Wests of New Zealand. (There's no Zonk to be found in this - such echoes are common in Toobworld.)
We meet Grandpa West in the 'Scountrels' series. Could it be that he was the brother of Jake Webster, who was working in Vienna back in the early 1970's? Could that have been an influence in the naming of Wolfgang West? It may have been the only way to acknowledge the family connection without giving away Jake's cover.
Just an idea......