I agree that naming something ending in _Click is probably a poor choice of naming convention, one that I wouldn't use. But apparently the OP did use that. You and I would BOTH say "shouldn't do that" - but the question remains, why doesn't it work correctly in the way it was used?
Paul and theDBguy have suggested alternatives. I'm actually on your side that smig should simplify the routine name. There, I think I have to agree with Paul that this is an execution-time failure. Because of the quotes in the string used to define the OnDblClick routine entry point, that can't be evaluated until you actually take the double click. This is an incredibly fine point. ME has no meaning outside of VBA code.
Smig suggests that this works as a "normal" function call, which is to be expected, because in a normal function call, you HAVE to be in VBA context. But the question then becomes, if ACCESS is preparing to make a call to ENTER an event context, is it in VBA context before the actual entry? I think the answer here has to be no. The "ME." that is part of the event linkage has no meaning because that linkage is in Access context, not VBA context, and so the activation fails.
Your "Me.name" substituted into the string (and change the formal argument from form to form-name/string) would probably work. The substitution occurs in VBA context so should sail right through.