Any ideas how to make this black part in blender?
With hair should work:
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Thinking it out…
High resolution image of the logo for weighting.
A couple of curves, thickened, perhaps converted to a mesh.
On an emblem shape, create a particle system that has weighting to only apply certain curves to certain areas. Perhaps that should be several particle systems; for your example a black and white system.
The curves are your stitches; scale to fit; just like in that kind of work, the more you have the thicker it looks/is.
Robert