The "Black Country" accent was well understood in B'ham as there were so many living there.Wolverhampton was very well known to everyone as there was a lot of business between to the two towns.The word Hampton appears all over England in many place names.There isn't anywhere in B'ham called Hampton,the closest being Hampton-in Arden in S.Warks.Many of the outlying streets were so named as that is where they led,many being coaching routes,ie.Lichfield St,Walsall St & Bromsgrove St.The street names you gave(Little Hampton St. & Great Hampton Row being others) are some of the oldest in B'ham and probable led to outlying villages ie. Nechells,Duddeston & Edgbaston.
Regards Jim & welcome to RootsChat.