Hahaha... I think there could be a UK site with a custom badminton bag option. If you're looking for a little customization, FZ Forza has bags with "My Bag" and it's a plastic covering over your custom tag (has a picture, country flag, and name OR other option is contact info i think). Other than that, you might have to get it done by a store/reseller.
Why would you need a custom bag Tbh I just go around with an under armor gym bag. I don't need to bring extra sets of rackets, just maybe another shirt, and a water bottle. But then again my strings never break. Its mostly because people give me dirty looks when I haul a big bag on to public transit..
its preference. so if you like your underarmour bag just stay with it. Percuzz wants a customised one so be it. ☺everyones happy