Smeargle in depth
The beagle that signs the walls
The English name combines smear, to spread or daub, with beagle, the dog breed that the design copies almost in full: short muzzle, floppy ears, and spots. The things that aren't dog are the tail, which ends in a brush, and the flat hat on its head, which gives it the look of an easel painter.
The Japanese name, ドーブル (Dōburu), has no agreed reading. Bulbapedia links it to double, because of the business of copying other Pokémon's moves; WikiDex prefers to read it as a blend of dog and doodle. The three syllables allow for both, and nobody at Game Freak has settled which one was intended.
One PP, forever
Sketch has never had more than 1 PP in any generation, and its effect is permanent: whatever it copies stays copied. The feature that sets it apart from every other signature move is that its owner relearns it on level-up, meaning a single specimen can fill all four slots if given the chances.
In Scarlet and Violet, things started out broken. Between versions 1.0 and 2.0.2, Sketch simply couldn't be used in battle; it started working again with patch 3.0.0, which also brought a longer list of exceptions. It can no longer copy Dark Void, Hyperspace Fury, Revival Blessing, or the signature move of Terapagos's Terastalized form, on top of what had already been excluded: Struggle, Chatter, Z-Moves, and Sketch itself. In Generation II, it also couldn't accept Transform or Mimic, a restriction that was lifted in Generation IV.
Copying without ceasing to be itself
There are three ways to borrow someone else's identity in this series, and all three work differently. Ditto transforms: it takes on the opponent's appearance, types, stats, and moves, but only for the duration of the battle and with its own HP. Kecleon changes type when it takes a hit, without altering anything else. Smeargle is the only one of the three that keeps the loot: it leaves battle with the move on its data, all 250 of its points intact, and the same dog face it had when it came in.
The practical result is that no two specimens are alike. The same Trainer can bring one with Spore copied from Breloom's line and another loaded with hazards, and in the game's data both show up as the same species with the same ridiculous stats.
What its Pokédex entries say
The Pokédex entries have hammered home the same detail since 1999: territorial marks, fluid from the tail, painted walls. Five thousand catalogued variants is a figure associated with no other species, and suggests that whoever wrote those entries took the joke of a graffiti Pokémon seriously. The pawprint on an adult's back points in the same direction from another angle: it's a companion's signature, not its own, and works as an age marker within the group.