I’m guessing that your UV seams are splitting the glass down the middle, right? What you need to do select the island that’s over your reversed text, then, in the UV window, right-click, and select Mirror Y.
That’s because you have baked lighting information in your texture that you’re using. If you wrap that around your model, you will get inconsistened lighting also if you rotate parts of the texture then of course, the lighting doesn’t fit anymore for the rotated parts.
Not much you can do tbh. You could try to extract/recreate that logo and put it as stencil/decal on your glass. You would have to texture the glass and foam on your own then.
I think it’s all dependent upon how you’re unwrapping it, maybe? I made a quick mockup to play around with, and I did it by grabbing the faces where I wanted the logo, unwrapped just those, laid them on top of each other, then aligned them over the texture, and it came out as expected.
Though WK042 is right though. The underlying glass should be it’s own material, with a transparent logo overlaid on top of it. Like so: