I believe Obi-Wan did remember R2-D2 in Star Wars: A New Hope. Throughout the Star Wars saga, we see that Obi-Wan has a close relationship with R2-D2. In the prequel trilogy, R2-D2 is often seen accompanying Obi-Wan and Anakin Skywalker on their adventures. As a Jedi Knight, Obi-Wan would have relied on R2-D2 as a trusted astromech droid, a companion, and a friend.
Obi-Wan’s relationship with R2-D2 is further emphasized in the original trilogy when Obi-Wan is still alive. In Star Wars: A New Hope, Obi-Wan encounters R2-D2 once again when he meets Luke Skywalker on Tatooine. When R2-D2 plays Princess Leia’s holographic message, Obi-Wan seems to know exactly how to activate it. This suggests that Obi-Wan remembers R2-D2 and is familiar with his capabilities.
It’s important to remember that Obi-Wan was not only a skilled Jedi but also a wise and experienced one. Jedi are known for their exceptional memory and ability to recall intricate details. Obi-Wan’s memory would have been sharp, allowing him to remember R2-D2 and his functions even after many years.
Furthermore, Obi-Wan’s connection to R2-D2 goes beyond their shared history. R2-D2 carries a significant amount of important information, including the plans for the Death Star. As a former Jedi Knight and member of the Rebel Alliance, Obi-Wan would have been aware of the importance of this information. It is plausible that Obi-Wan would have kept himself updated on the whereabouts and activities of R2-D2, making it more likely that he remembered him when they crossed paths again.
Based on Obi-Wan’s past relationship with R2-D2 and his familiarity with the astromech droid’s capabilities, it is highly probable that Obi-Wan remembered R2-D2 in Star Wars: A New Hope. Their connection and shared history would have allowed Obi-Wan to possess the knowledge to activate Princess Leia’s message and play it for Luke Skywalker.