I think it varies
I think it varies depending on who produced the furniture. I have a set of Mogensen chairs made by Søborg Møbler but they don't have Mogensen's name on them anywhere. I believe that other companies also produced his designs.
The link is a photo of the SM label. (The flash washed out the word "møbler".)
Of course, not everything made by SM was designed by Mogensen, either. I think that most Danish designers' names are not on their pieces. Hans Wegner's name often is, but I have a rocker designed by him with only the FDB mark, not his name.
I think you just have to know Mogensen's designs well enough to spot them and then use whatever labels are present to confirm it.
My Mogensen
furniture is made by Frederica mobelfabrik and has a double label, one with the two "F" logo the name of the manufacturer and the name of the designer on the last line.The second label is a printed frame next to the double "F" logo with hand written numbers, obviously relating to the time of production. Spanky is right I think in assuming that each manufacturer had his own way of labeling.
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