Peter's Pals Designs is fine. Designs by Peter's Pals is also a possibility.
The brand name--or sub-brand name, if there is such a thing--is what it is, and it does not change.
Peter's Pals is not about pals, literally, but pals figuratively. For that matter, Peter's Pals is not about Peter, literally, but only about Peter as a brand name, which in this case is Peter's.
Take the brand name Smothers Brothers. (There are actually two brothers whose surname is Smothers, but as far as I know they are not in a business named Smothers Brothers, though Dick Smothers does have a wine-making business.) If the two brothers were in the wine-making business together, and they decided to name their company Smothers Brothers Wine, the same rule as above would apply. The brand name is what it is and is not inflected to show possession. The wine's brand name is simply Smothers Brothers.
If the vintners Smothers decided to have a sub-brand (or niche brand) such as Smothers Brothers Varietals, the same rule applies: No possessive is needed; their niche brand is Smothers Brothers Varietals. Other examples:
- McCurdy Family Ford (a car dealership) might have a niche brand called McCurdy Family Ford Compacts [i.e., compact cars], but not McCurdy Family Ford's Compacts.
- Galaxy Sound, a business involving retail sales of stereo components, might decide to branch out and create a specialty business within their stereo music reproduction and call it Galaxy Sound Surround Systems (for home theater customers). Again, there is no need to make Sound possessive. -