Apparently it originates from the town of Gaddesden in the shire of Hertfordshire in United Kingdom. Meaning Gads den. The place where gad lives.A place called Little Gaddesden, and Greater Gaddesden still persist today
Even more hyperthetical is the rumour that Gad was of Scandinavian origin thus putting him amongst the invader populace, probably from Denmark with other Vikings. The crossing from Denmark to England being relatively easy across the North Sea.
Gad is the probable family name and could be from multiple people who settled here. It means a goat,i.e.a gaet, from the scandinavian, there then follows the den part being the place where the Geat's lived.There is a great presence of Gadsdens still living in Hersfordshire and surrounding counties. Not a very adventurous lot