Best way to add this simple label on a bottle

I have this bottle

I would like to add a label on the blue square, but if i assign a material to the faces overlapping the square, its the whole face that will get affected.

i got close by projecting uv map from view, scaled everything to fit the label on the portion i wanted, then for image texture i turned clip instead of repeat, which gives me a black background instead of the color of the rest of the bottle, on top of that subdivision modifier messes the image as it becomes round.

adding geometry (either loop cuts or knife cut) is also not good, if it was possible to draw a uv map without changing geometry thats what i would have done but now i have to find a good way to do that, (maybe assign the texture to a different plane then shrinkwrap) ?

thanks for your answer, I didn’t formulate my question clearly, I have solved the problem since and sharing my solution here although im not sure if its the best way to do it.

the problem was this

the transparency in the logo got mapped as black, i wanted it to be mapped to the base color of the model.

first i set up the base color like so in order to group those values together and reuse them in other materials

the group is set

in the second material that has image texture i mix the colors using alpha from image texture as factor, meaning if alpha is not 0 use image otherwise use whatever is in slot A

using the created group to pull the color as well as other values i used (metallic and roughness, those i plug directly into the shader).

the black is replaced with the base color, but i wonder if this would work with more complex shaders (gradients other image textures for example, will try later)