R2-D2 is arguably the most heroic character in the Star Wars universe. Where other heroes have faltered, R2 has almost always prevailed. He is responsible for saving the heroes of the Skywalker Saga countless times. It looks like Artoo's legendary actions may have been used for inspiration for the droids of the Resistance.
In 2018's Star Wars: Poe Dameron #28 by Charles Soule, Angel Unzueta, Arif Prianto and Joe Caramagna depicts a rare quiet moment aboard the Millenium Falcon as BB-8 is telling R2-D2 his point of view during the destruction of Starkiller Base. Artoo had been operating in low-power mode during the majority of the events that take place during The Force Awakens, so it is possible he is hearing the story for the first time.
BB-8 paints a dramatic atmosphere of the mission. He makes it clear that they went into First Order Space prepared to die. Artoo apologizes to BB-8 that he couldn't be present during the mission but BB-8 assures the droid that he has already put in his time. BB-8 comes off as extremely child-like as he explains the mission. The young droid shows despair when describing the losses that the Resistance suffered during the battle. Artoo thanks BB-8 for sharing this information with him before their conversation is interrupted by C-3PO.
It appears that R2-D2 sees potential in the young droid and believes that he is a valuable asset to the Resistance. This story depicts Artoo as extremely wise and comforting. BB-8 is very excited to tell Artoo this story but also appears nervous at times. Artoo is able to keep him calm and explain that as long as they have General Organa, hope remains. The two droids also bond over their admiration of Han Solo. They both witnessed him perform heroic feats that inspired them to be greater. Though, they do both agree that Han Solo was a bit reckless at times.
It's interesting to note how familiar BB-8 seems to be with R2-D2's past. The two only briefly met in The Force Awakens and Artoo quickly left to escort Rey to Luke's location. There wouldn't have been time for BB-8 to learn R2's story from the firsthand source. Artoo was supposedly in low-power mode from the moment that Luke disappeared, which leaves little time for BB-8 and Artoo to communicate before The Force Awakens. It's entirely plausible that Leia and other leaders of the Resistance were sharing Artoo's history with new droids to breed inspiration. R2-D2 did more than any other droid during the Rebellion and played a vital role in toppling the Empire. It would make sense that R2's past would be told to all Resistance droids, persuading them to believe in the cause.
R2 treats BB-8 with much greater respect than he shows other droids. He is consistently shown bickering with C-3PO as they only cooperate when it is absolutely necessary. Additionally, Artoo and Chopper almost immediately became nemeses in Rebels. Even though their personalities clashed, R2 still held enough trust for Chopper and followed him aboard the Ghost. R2's communication with BB-8 is truly unique and shows that he cares for and respects the young droid. It would almost appear that R2 is bringing BB-8 under his wing as a mentee.
BB-8 brought a much-needed new look to droids when he first appeared in The Force Awakens. The prequel trilogy brought back R2-D2 and C-3PO to represent the droids, so BB-8 was a refreshing new touch. The soccer ball droid is responsible for kicking off the events of the sequel trilogy, much like how R2 kicked off the events of the original trilogy. It makes perfect sense that R2 would begin mentoring the young droid since their backgrounds are so similar. BB-8 is to Poe what R2 was for Luke, so to speak. Artoo truly inspired BB-8 to be the greatness that the Resistance needed to overcome the First Order.