Need name

i know the benko and this can transpose to benko...but what do you think of it and do you have any name suggestion?

Yes it looks like a bastard child of the Benko gambit LOL yeah theres your name for it: Benko gambit "bastard child variation"

it came to me when i was trying some d4 surprises for blitz.i searched about it and i couldnt find a name for it although i found about 5 games which transposed to benko style games and since this has no official name i think that i can give it a name myself althoughit will probably not be official if i dont use it at a tournament...anyway i searched about dzidzi indian and i couldn't find a so called defence

Dzindzi Helped out Lev Alburt with his openings in his 1990 US open championship. I don't know the exact line, but ...a6 was played quite early in it.

i dont think the bastard child variation will be a good name....because what will my opponents say ? i lost to the bastard child variation????:P ok idon't think it will have much success for a slow game but in blitz it may catch my opponent by surprize

The problem with your line you might see in your 2nd variation.
White should not play 4. e3? Instead he should play 4. cxd5 and if 4. ...Nxd5 then 5. e4
Or if 4. cxd5 Qxd5 then Nc3 and White tempos off your queen.
Which position are you referring to with 7. ...Bxb5
The first diagram with absurd variations...
EDIT: Never mind, it was deleted.
This was the diagram that was deleted, well deleted, because of course, it doesn't make any sense.

@ ponz111 after 4.cxd4 cant i play 4...c3 5.dxc3 Nxc3 and with the pawn on a6 square i can avoid the Bb5+
1.d4 Nf6 2.c4 a6 need a name for it....