Akuma's Comics: The glitch Ashura the Hedgehog has a major ax to grind with Shadow as he feels he deserved to be Sonic's fake and Evil Counterpart in Sonic Adventure 2, not him. Shadow couldn't care less about Ashura and just wants him to leave him alone, rebuffing his attempts to be a rival and telling him to get a life.
Bravoman: Anti-Bravoman tries to play himself up as a dark anti-heroic rival to Bravoman, who goes about without noticing him, when he does find Anti-Bravo, he befriends him and still remains ignorant to Anti-Bravo trying to set up a rivalry. When Bravoman goes to an alternate Dimension where Anti-Bravoman has leveled the world all in the pursuit of power he tells Anti-Bravoman that he can be a real threat, and to keep up the good work.
Played straight in Cosmic Dash where the space pirate Vid Seng, and by extension his larger crew, has a rivalry with Dash Kameku and his cohorts. Dash doesn't see Vid so much as a rival but more of an annoyance... when and if he remembers him.
Jango Fett from Darths & Droids is the Unknown Rival to Obi-Wan Kenobi, complete with Obi-Wan saying "Sorry? Do I know you?" as Fett prepares to gloat about his plans for revenge. Although unlike many of the other examples on this page, Obi-Wan really has never before met or seen Fett, or indeed had any inkling of the man's existence. Fett is well aware of this too, and takes great pleasure in watching Obi-Wan squirm while trying to figure out why this random bounty hunter is trying to utterly ruin him.
In Dumbing of Age, Becky sees Dorothy as her implacable rival for Joyce's affections. (Platonic affections; Becky is gay and in love with Joyce, but knows that both she and Dorothy are straight.) Dorothy sees Becky as another of Joyce's friends, who's a bit weird around her for some reason. This eventually gets developed to the point where Dorothy know Becky thinks of them as rivals, but doesn't take it seriously, and it increasingly appears that Becky doesn't entirely take it seriously either and it's just becoming a bit.
Becky: So I betcher wonderin' why you're invited. Well, I keep my friends close but my enemies closer. Dorothy: Becky, we're not enemies. We routinely come to each other for advice. Becky: Do you prefer cheese pizza or pepperoni? Dorothy: Pepperoni. Becky: Then you're only allowed cheese pizza, nemesis.
Las Lindas has Alejandra to Mora. This is more a Deconstruction of the trope, since Mora doesn't really care and is more worried about keeping her farm up and running, Alejandra's near-overwhelming desire to crush Mora into dust mostly just harms her mental state and her company's reputation and financial state.
Nebula: Jupiter devotes the majority of his waking moments to trying to find a way to kill Sun and take his place as leader. Because he's incredibly obvious about it, Sun knows, but finds him to be so little of a threat that he's just vaguely concerned about the possibility of Jupiter injuring himself in the course of a Zany Scheme to try and kill him instead of holding him as any sort of serious rival.
Main character Roy Greenhilt is the Unknown Rival of the Big Bad Xykon, who's vaguely aware that there's a guy called Redpommel or something who swore revenge on him for some reason or other. Even after Roy personally thwarts his plans and destroys his body and lair, the most he gets from Xykon is the page quote. Double Subverted later when Xykon makes a Call-Back to his last encounter with Roy... except it was All Just a Dream. When Xykon actually faces Roy again in the desert, he's already forgotten everything about him.
Interestingly, Redcloak, who isn't the Order's main target, actually recognizes them every time they meet, and even gives Xykon a recap of their previous fights when they arrive at the pyramid. Even he is a bit fuzzy on who they are beyond a recurring enemy, though. The Monster in the Darkness doesn't recognize them at first, but remembers the name of the Order, and when in the desert, actually recalls Roy (alias Flopsy).
Also the case with Ian Starshine, who thinks his own plan to topple Tarquin is significant to the latter, to the point that he (falsely) believes that Elan was sent by Tarquin to infiltrate the Order of the Stick to get close to Haley and then, by extension, Ian himself. The real reason Ian was being held by Tarquin? Bozzok was paying him to. Other than that, Tarquin didn't care about him. Tarquin does later frame Ian for assassination, but it's over a petty argument and to "test" Haley, more or less the opposite of what Ian imagined. Although Tarquin does state he vaguely remembers Ian at one point (but not his name), so he may be partially right.
The trope is Played With in regards to Tarquin and Julio's rivalry. The two men are fairly powerful characters in the context of the story, Julio being a world-famous adventurer and Tarquin being a feared dictator that's gradually conquering a continent with his friends. Both men also serve as foils to one another in the story being Genre Savvy father figures to Elan. However, while the pair do have a rivalry, Julio considers Tarquin to be a B-list villain while Tarquin sees Julio as more of a nuisance and obstacle to his goals rather than an arch-enemy.
In Questionable Content, Hannelore's archenemy is a woman who lives in her apartment building who left a pair of underpants in the washing machine, meaning OCD Hanners had to get rid of all her clothes, and was later spectacularly rude to her in the coffee shop. The woman did not interact with Hanners the first time, and barely acknowledged her the second time (which was the problem), so she's completely unaware of this.
Inverted in Shortpacked!, Sydney Yus has a whole speech about how Galasso will remember her now, which she insists on saying despite Galasso making it clear that he knows exactly who she is and always saw her as his most dangerous enemy.
In Something*Positive, Ollie sees Davan as his Arch-Enemy. Davan wasn't even aware that Ollie hated him until Ollie recently confronted him and declared that they were enemies. This is because Ollie blames Davan for derailing Ollie's theater career years ago when it was really Ollie's own incompetence that did it. Davan is actually a bit upset by this.
Van Von Hunter has a recurring character named Vengeance Joe who swears revenge against the title character... for failing to introduce himself when they passed on the street.
In The Wotch, Cassie is this to Anne. Anne is oblivious to most of the goings-on in her world and just sees Cassie as a friend, not realizing that she's jealous about Robin's affection and Anne's magic power, which Cassie thinks Anne did nothing to earn. Though Cassie later wins Robin, she's still upset about the magic thing.
he remembers him.