How can you remove markings from a headset?

If the item is laser-etched there will be a slight recess in the material. Nothing will remove that short of filling it in with autobody fill/bog, sanding smooth, and then painting the whole thing.

You could make it more discreet by simply painting the part with spraypaint, the same colour it already is.

If the logo is a decal you can use very gentle heat to soften the adhesive and then acetone or any goo-removing product to melt the adhesive.

Another simple option is to cover that part with something useful, like a headlight or a bike computer/headunit.

Is too late, but you could also prefer to buy parts that don't have the logos in the first place.