Is it possible to believe in false gods?

The Big Three monotheistic religions (especially Judaism and Islam) make a point of instructing their adherents not to worship false idols or false gods. But does Yahweh/Allah expend his energies futilely?

Suppose I was an Israelite living at the time of Moses, and I worshipped a Golden Cow. Isn’t the name “Golden Cow” just another name for God (to me), just as Yahweh and Allah are different names for the same thing? Presumably God is jealous because he thinks that he should be getting the credit for Creation. But surely being jealous of a Golden Cow is only admitting the existence of a holy Golden Cow! Otherwise, he should hardly be angry with me: he should merely be telling me that he doesn’t look like that. But me being mistaken about his appearance should not be construed as blasphemy: if I am worshipping the Golden Cow, presumably I think he is great no matter what he looks like—and you can hardly ask for more respect than that.

If God expects his followers to worship him on the basis of the correct name and appearance, surely it is only courteous to introduce himself to them personally?