I don't consider it to be arbitrary. For generations going back to the late 19th century important coins were known by the name of the collection they were first found in (or in a few cases the first famous collection) and they woud continue to be known by that name even as they moved from collection to collection. The reason was it made it much easier to trace pedigrees. It has only been in the past 20 years or so that important rare coins have started changing their names every few years as they moved from person to person. It has made keeping track of which coin is which when you have a coin with ten or fifteen surviving specimens but they go by 20 or 30 different names. In the case of the 1913 nickels they were all kept together until 1943 and then each became known for the person that bought it out of the group. (one exception is the Eliasberg coin which really should have been known as the Newman coin.
http://uspatterns.com/j1790.html thought this was interesting since it was with the big 5 for some time...
If the only reason is to be able to trace pedigrees, then having a name that transcends ownership should be more desireable not less. Regardless of who owns the coin, it will always be the Hawaii Five O 1913 Liberty Nickel!