The 1..d6 opening by Black doesn’t have a name of its own, but depends on what White played first. It may become a number of other openings by transposition:
The d6 opening may also become some other lines of independent merit (e.g. 1.d4 d6, 2.Nf3 Bg4!?).
Against 1.e4, the Black move 1..d6 is likely to become a Pirc Defence, or perhaps a trendy new type of Philidor Defence.
Diagram: Pirc Defence
Diagram: Philidor Defence (Trendy Queen Swap Line)
Against 1.d4 by White, the move 1..d6 is the start of the Old Indian Defence (if White plays 2..c4). Or White can play 2.e4 and it becomes a Pirc Defence (as above).
Diagram: Old Indian Defence
Diagram: Old Indian Defence with Bg4
Against 1.c4 (English Opening) by White, the move 1..d6 may start a Dutch Defence (with Black playing e5 and f5 like a Reverse Grand Prix Attack), or it may become an Old Indian Defence.
Diagram: Dutch Defence against English Opening