Your UV mapping looks difficult to apply a texture to. Especially because it has so much empty space, and is skewed in an arc, so you would need to warp all your textures for them to fit nicely.
You should make the UV mapping work for you. Why don't you use the built-in CylinderBufferGeometry
class to apply a texture on top of your cup geometry? You could use its attributes to match the side of your cup's shape:
CylinderBufferGeometry(
radiusTop,
radiusBottom,
height,
radialSegments,
heightSegments,
openEnded,
thetaStart,
thetaLength
);

With this approach, you could leave your cup geometry untouched, then apply a "sticker" texture on top of it. It could wrap all the way around the cup if you wanted, or it could be constrained to only the front. You could scale it up, rotate it around, and it would be independent of a baked-in UV mapping done in Blender. Another benefit is that this approach occupies the entire [0, 1]
UV range, so you could simply use square textures, and you wouldn't be wasting data with empty space.
Look at this demo to see how you can play with the geometry's configuration.