How to tame my Baby Green Iguana?

What you're doing is good! :) Maybe you could try holding a favorite treat in your hand and just see if your ig will come to it. Just slowly get closer to touching it, I don't think you really need to do a lot more. And for the name, Iggy is so cliche and common and stuff... I say Gizmo, or just wait until you can see its personality more. Good luck with your new baby! ;D