I swear Wander has OSDD and I can prove it. Not only that, he's polyfragmented.
First, to clarify, the reason I think Wander has this specific disorder, and not full DID, is that he doesn't appear to have amnesia gaps between switching unless the situation he was dealing with was particularly stressful. Plus, he can tap into multiple alters at once.
Next, Wander switches between "personalities" or alters multiple times throughout the series. The way Wander holds himself and talks change drastically and consistently, even down to the way he looks. His priorities and opinions shift, to the point where he argues with himself.
Lastly, the biggest evidence that Wander has alters is the episode called "The Wanders." Showcased is Wander entering a magical cave that "splits" multiple versions of himself. The whole episode features the different alters of Wander that are shown throughout the show.
They literally are "fragmented" in dozens of gems.
The whole theme of the episode is that "every Wander is needed and important", and in order to unlock the "main" Wander they all have to unify and reunite. Just like alters need to work together in one body in a system.
Even a part of Wander who stirs chaos and does "the opposite of what is said" is valuable. He is shown throughout the show going against Slyvia's wishes and messing with Peepers and Hater. One prominent episode of his would be "The Prisoner."
Canonically, Wander has 420 parts. Some of these them include:
Super hero Wander. This alter was featured in "The Boy Wander" and briefly in "The Battle Royale." He has a deeper voice, carries himself very boldly, and seems to have a strict sense of right and wrong. He doesn't trust Dr Screwball Jones because he "forces people to be happy."
Blonde Wig Wander. Notably a feminine leaning part. This alter is mostly shown for brief moments in episodes, such as "The Greatest." She seems to have a seductive way of walking that is very distinct from the others.
Bad Guy Wander. Similar to Hero Wander, this alter had a episode dedicated to him: "The Bad Guy." He acts cartoonishly evil, has a deeper voice and a "gremlin" way of moving around. His only goal seems to be to "act evil."
Sad Wanders. These alters are likely the reason Wander can act outwardly perky despite having a system. I think it's possible that they hold onto memories, depression and other pained feelings that come from trauma.
Fur Picking Wander. This alter seems to hold onto to "dermatillomania", which Wander taps into when he is VERY stressed. This is heavily featured in the episode "The Box." It is notable that this condition is common in people with trauma.
And MANY more, such as: Easily Impressed Wander, shown in "Lil Bits" and many other episodes. Zen, Hippie and Affectionate Wanders, three alters he taps into very frequently. Hyper Cleaning Wander. Nerdy Wander that has an archive of knowledge. Dancing Wanders. Banjo Wander. Etc.
Finally, what is most telling is the ending of the episode. When Wander is seemingly reunited with all of his alters, he tries to go off to "stop the evil Lord Hater." Sylvia immediately knows something is wrong, and goes to finds who's missing. What she spots? An inner child.
Not only is this child curled up, he looks terrified when Sylvia approaches him. This implies that Wander was deeply wounded as when he was young, which matches the criteria of OSDD. Wander does NOT want to have this child back at first, and shows visible fear at the idea of it.
Yet, when they renuite Wander mentions that he considers the child "the most important part." Not to mention, the very thing that drives him to help is the fact that he was "once helpless."
The end message is clear. Wander had severe trauma happen to him as a child, so he wants to help people who HE thinks had trauma too.