Change position of the texture on a layer(mesh)

UV mapping/unwrapping is the best approach, there are two other options I can think of.

1_ MultiMaterial: create a second material, set your group draw range, targeting the area you want your texture over, effectively redrawing the texture over the first material.

2_ use decals: with some draw backs (here and here and some others), check the examples discussed in the thread below.