It's just called The Vape Shop - they have a website (not sure I can put it on here so won't for now!!), the shops are in the Sovereign Centre in Boscombe and then another one in Wick Lane in Christchurch. There's also a little old fashioned Pipe/Smoking shop in Southbourne with a selection of liquids and a few bits.
You're in a lucky area for juice.
Triphammer Juices is based in the Vapourmax shop in Kinson and is staffed by keen vapers/certified loons
If you are more Christchurch way try Vapourway in Purewell, also Triphammer stockists and also run by great people.
Both have active Facebook pages if you want to join in
Oddly enough the aforementioned pipe shop also stocks Trip's stuff too
My experience of the Sovereign center crowd is not great but I have never tried their juice