Hi kariomart,
The same size wouldn't be an option, as the UV space is normalized to the image. In short, if an image is 1024 x 2048 and the UV setup is that all are covered by it, then the UV space stays in 0-1 normalization but adapts to the image. Which subjectively appears to be a normalization to 2:1, as it is a translation from 2D information towards a 3D object. (Deformers can change the size while not affecting the UV.)
The simples way is to calculate the point where it stops, and cut there, make a selection, and fill the whole UV 0-1 space with the UV, so the selection provides a clear framing. Not simple to explain or suggest that for general use, but here is an example:
https://projectfiles.maxon.net/Cineversity_Forum_Support/2025_PROJECTS_DRS/20250921_CV4_2026_drs_25_TXrc_01.c4d.zip
I am sure some would like to point to Texels. Here I'm not sure if that would work as you need it.
https://help.maxon.net/c4d/2025/en-us/Default.htm#html/Texel_Density.html?Highlight=Texel
What I have done in the example file below:
The height was easy to explore
Then I selected the partial circle (Edge to Spline). With a quick XPresso set up measured the length.
This allowed me to calculate the needed Pixel for the horizontal Length. X = 670x401/203
Since the label would cover the polygons completely, that was the fastest way for me.
Relax the outer UV Polygons and use the Command "Fit UV to Canvas."
Now the new texture (401x1324) wraps around the full outside, while keeping the Label intact.
I colorized the extra space, but that can be just empty.
Example
https://projectfiles.maxon.net/Cineversity_Forum_Support/2025_PROJECTS_DRS/20250921_CV4_2026_drs_25_TXuv_01.zip
Enjoy your Sunday