The simplest explanation would be that Luke did try to find out about the Jedi, but didn't know what he was looking for.
From Luke's perspective, Yoda is one of many members of the Jedi Council. All of them are presumed dead and several belong to alien races. He didn't have any reason to research Yoda specifically.
Obi-Wan could have told Luke on the Millennium Falcon, but was waiting until the time was right. If Luke knew that Yoda was alive, he might have let something slip, which could have gotten back to the Empire, who would have gone looking for Yoda. Obi-Wan and Yoda wanted time to train Luke on Dagobah without being disturbed, so Obi-Wan didn't reveal Yoda's location until he wanted Luke to go there right away.
Exactly why Obi-Wan waited a few years after his own death to tell Luke is not explained. Maybe it took a while for him to master Force-ghosting well enough to communicate with Luke. Speculating wildly, the fact that Luke himself was near death at the time might have made it easier for Obi-Wan to make the initial contact.
A few other significant factors:
- While there might have been records of Yoda's appearance on Coruscant, they would not necessarily be reproduced in the remote backwater systems where the Rebellion was hiding.
- The Empire had actively been trying to suppress knowledge of the Jedi for twenty years. It would be like trying to research the victims of Stalin's purges in the USSR, while Stalin was still alive. You can't just walk into the public library and look them up, and asking about them (in systems where the Empire holds any influence at all) would likely draw unwelcome attention. If Luke did find anything, it would be difficult to separate reality from Imperial propaganda.
- Luke was part of a Rebellion which was fighting desperately for its existence. He might not have had time to do much research into the Jedi. By way of comparison, Han Solo didn't have time to visit Jabba the Hutt and pay him off to remove the price on his head -- and avoiding bounty hunters might be considered more urgent than researching (presumed) long-dead Jedi Masters.