Nothing new in re-badging. My own club, and later I, owned a 6" x 30 BGSC lathe with IXL embossed on a plate rivet-screwed to the headstock.
6" centre-height that is. I don't use the diameter convention.
According to Mr. Griffith's excellent site, "IXL" never made anything, and the lathe was actually a German-made Ehrlich, probably of 1930s vintage.
I donated it to Lynton & Barnstaple Railway workshops quite some years ago now, and I hope it's still in service if not there, in another caring home!
Simiarly, I have seen a small horizontal miller badged (if I remember aright) "Patrick" or something similar; certainly not a name listed on lathes. co; but I am pretty certain it's an Denbigh H4 of which I own an example. Denbigh did make machines or others, and it seems to have been quite a common practice long before the days of Axminster / Warco / Clarke et. al.