Naming someone after the Pinkertons is dark as hell. The fact that it could be shortened to "Pink" makes it even more sinister and messed up, like trying to give the KGB a cute makeover.
So that's interesting!
Rosamund Pinkerton aka
Rosie Pink would be a superb name for someone who may seem sweet as pie and respectable but is actually someone who will do anything for the right price, that kind of thing.
If you wanted to keep things genuinely cute I'd go with something like
Rosamund "
Rosie" Pinks, after the flowers (dianthus, aka "pinks").