Galar's Gym Badges names are so boring!

I would be ok with the simple naming convention if there weren't called "badges." Like, this is a big sports thing, I feel like "medals" would have worked better. Especially the way they all connect together into essentially one big medal.

While I do agree that "medals" would be more appropriate, given how each one is a fragment of a larger, complete medal, the term "Gym Badges" is pretty deep-rooted in the series. From Kanto to Kalos, every Gym has had a "Badge" as it's ultimate prize in order to compete in the league. While, back then, it all made more sense, given the fact that each badge had it's own unique design and name (well, most of the time, such as some of Kalos' badges having meh-ish names), so it would better fit the "badge" title.

Alola is the only exception due to the nature and culture of the islands. For them, the Island Challenge was a rite-of-passage and little more, so residents would take "trials" to prove their worth. Alola didn't have an actual league for a long time until Kukui decided to make one, and you, the player, effectively gave birth to it (that sounded strange) by becoming the first Champion of it. So, given Alola's culture and nature, it's the "black sheep" of the Leagues by that standard, but since it only just "recently" gained one, it gets a pass.

Here, in Galar, where the Gyms are the focal point of the region, the reason why they went with "Badges" over "medals" is pretty much tradition and a deep-rooted part of the franchises history. Again, I agree that "medals" would be more fitting, but, overall, since these are Gyms, it's only natural for the franchise to use its tried-and-true term of "Gym Badges" over diversifying the name of the "prizes" for the second generation in a row. So, generally speaking, it's probably better they kept the term "Gym Badges" over "Gym Medals" due to how the franchise structured itself over the years, with Alola being the only exception due to its vast nature and culture differences, along with the fact they didn't have an established League until the PC came along and helped shape it. That's how I see it, at least.