There are a number of variations of thename mainly due to misspellings when people were not very literate. My name has been spelt Binney, Binnie, Bennie etc over the last two centuries. Most Binnies/Bennies were found around the Falkirk/Clackmannanshire/West Lothian area of Scotland originally. Many are later found in the Glasgow and Edinburgh areas with the name spreading further and wider during the 1800s. My own family came from Alloa in Clackmannanshire.
Sorry if this is too late but I've only just found this site.