Wooper in depth
The axolotl named after an axolotl
In Japan, the Mexican axolotl is popularly known as ウーパールーパー, wooper looper, a commercial name that became popular there in the 1980s. That's where everything comes from. The Japanese ウパー (Upah) is the shortened version of that name, and the English Wooper is simply the first half of it. There's no hidden pun or mythological reference: it's named after the animal it's based on, and that animal is an amphibian that keeps its external gills for life instead of losing them when it reaches adulthood.
That explains the design better than anything else. The three points on each side of its head aren't decorations or ears, they're gills, and the lack of arms recalls salamander larvae before they develop their front limbs. The only feature that distinguishes males from females is right there, in the size of those gills.
When the line split in two
For six generations, this was a two-stage line: Wooper at 20, and that was it. Scarlet and Violet introduced the Paldean form, which is Poison- and Ground-type, brown instead of blue, and has hardened gills, along with a Pokédex entry explaining that it lost a territorial dispute and moved to living on land. Its evolution is Clodsire, with 130 HP and 100 Special Defense compared with the 95 and 65 of the usual Quagsire.
The interesting detail is that both forms share Unaware as their hidden ability, and both retain Water Absorb even though the Paldean one is no longer Water-type at all. The original version kept Damp as its primary ability; the Paldean one replaced it with Poison Point, which fits the poisonous film the entries have been mentioning since Generation II.
What to do with it in a normal playthrough
As a travelling companion, it's patient. It learns Mud Shot at level 8 and Slam at 16, and up to that point it doesn't hit anything particularly hard; the real jump comes at 24 with Aqua Tail and at 28 with Muddy Water. Earthquake, its best attack, doesn't show up until 40, by which point it's normally already a Quagsire. With a Medium growth rate, it levels at the same pace as most Pokémon, without the late-game advantage of the Medium Slow group.
Its real early-game use is something else: its Electric immunity. In Johto, where Electric-type Trainers and Water Pokémon are everywhere, switching in without taking damage and answering with Earthquake solves situations that would cost someone else half their team. Against Barboach, the other early-route Water/Ground Pokémon, it takes hits better and deals less damage.
It debuted in Gold and Silver in 1999 and has appeared in almost every game since, with the notable exception of Generation VII, where it is absent. Catch rate 255 and 8.5 kilograms: between how easy it is to obtain and how little it asks of you, it's one of those species you catch without thinking and leave in the PC box.