I have several M&M numbers and I am never totally sure which one I should use as the primary number, probably the one at the bottom of the credit card. But they all seem to come back to the same place without any problems. The M&M service center doesn't seem to be worried about it, anyway. I suspect that if you move around a bit, as I have done in the past, you end up getting allocated a different number according to where you live.
Much less talked about is a shorter number associated with the M&M account, the Miles & More Customer Number. I have occasionally been asked for this, but I do not have it by memory. Could be that it provides an extra security layer.