My theory.

Does Bender have NPD?

Does Bender Have NPD?

A bending unit from Mexico, Bender is a robot who works for planet express with his coworkers, Professor Farnsworth, Turanga Leela, Philip J. Fry, Amy Wong, Hermes Conrad, Dr. Zoidburg, and Scruffy. He is a huge narcissist. Often chanting "Bender is great!" when doing tasks. Bender lacks empathy, not able to understand other people's feelings as shown in the episode that Dr Farnsworth gave Bender Leela's emotions. Bender thinks extremely highly of himself, often feeling the need to remind other how he is superior and needing constant attention or affirmation.

Bender has sociopathic tendencies. He will often use others, even the people who are "close to him", for his own gain. He has expressed that he has no issue with murder, stealing, or torture. And he often speaks or even brags about "Killing all humans."
As people with NPD often do, Bender hides his insecurities behind his narcissistic exterior. His flaws such as not having a back up unit, his fear of being forgotten or replaced, or his crippling self awareness about realizing he has no free will.

In a way, he feels like everyone admires him. In episode 12 season 5, the planet express crew goes camping. Bender tricks Fry into thinking he's Bigfoot to lead Fry into the woods and away from his tent before crawling into Fry's tent and falling asleep inside. In the morning when Fry comes back to camp without a nose, Bender assumes Fry chopped it off to look more like him.

Bender is incapable of loving in a normal way. Bender has a love of Turtles, because they remind him of himself in the way that, when they fall on their back, they cannot get back up. Bender had a love for his son, Ben Vending Rodriguez because Ben was a part of Bender. Because Ben looked up to Bender and considered him a hero, a great father, a fantastic role model, when in fact bender was nothing of the sorts. Bender treated Ben the best he could because Ben was constantly looking up to him, and wanted to be a Bender like him. After Ben loses all memory and goes to Bending college, Bender seems to completely forget about him. Never mentioning him in the show again.

Bender's ability to move on from dating people so quickly further proves my theory. From random hookerbots on the street, to the don bot's wife, Fanny, to calculon, Angelyne, and even to the planet express ship and many more. These are all examples of relationships bender has had that have only lasted an episode. In the case of Angleyne, Bender was so insecure that she still had feelings for her ex husband that he gaslighted and tricked her into getting back into a relationship with him.
Most of the ladies(and guys) bender has had a relationship with, he was told that he couldn't have them. Or they were out of his league in some way. Like dating them was a challenge that he would win, and then move on to the next. Inflating his ego.
This concludes my theory that Bender Bending Rodriguez does in fact have Narcissistic personality disorder.