Is this a popular variation/continuation of the Sicilian Defence? I've grown fond of playing this opening with black against e4. I know it starts with the Sicilian but if it has a name or some background that would be nice to know.

[FEN ""]
1.e4 c5 2.g3 Nc6 3.Bg2 b6 4.b3 Bb7 5.d3 Qc7 6.Bb2 f6 7.Nf3 e5 8.O-O O-O-O
No, it is not popular. 2.g3 is already only the tenth-most common move. It is apparently technically called the Steinitz Variation in ECO though it's not common enough for that to be a well-known name. It seems to often transpose to the Closed Sicilian, which starts with 2.Nc3 and usually results in White also fianchettoing (putting on g2) his light-squared bishop, though the knight usually ends up on e2, not f3.

In any case, ...b6 as a response is not seen at all in my database. ...b6 is not very common in Sicilians since Black usually tries to get in the more ambitious ...a6 and ...b5.