My friends and I call posh people (you know, the red trouser types) “Tobys” because we associate it with that type.Barnaby and Barney are definitely more upper-class, posh boy names!
Tobias/Toby not quite so much - and although there are names that seem to be used mroe regularly got dogs than children, i would definitely class Tobias/Toby as more a human name than a dog name!