What is the Go binary that Pulumi will search for to create the infrastructure? Is it the project name as listed in Pulumi.yaml?

Yes, but you don't need to build a binary. By default we will execute your program via

go run

if we don't find a matching binary.

If I cross compile for multiple platforms and distribute the binaries (to be investigated how that wold work) could it pick up the correct binary with the GO_ARCH suffix?

For windows we search for an .exe, but make no distinction for linux/mac: https://github.com/pulumi/pulumi/blob/c28c6022472572c71875ef2e7e3d5a35f7ea3c96/sdk/go/pulumi-language-go/main.go#L45