I Can Hear The Heart Beating As One is probably their best album, but I celebrate their entire catalog. Outstanding live act as well. IMHO one of the very best albums of all time: https://m.youtube.com/playlist?list=PLYWbEdTxWlSGIW5gn-ZCWdBGpL4issjEj
The name came from a story Richie Ashburn told about playing outfield (Phillies) with a guy that only spoke Spanish. Yo la tengo means "I got it". Ashburn learned the phrase because he had one too many close calls with colliding into the other guy. Ashburn had some funny story about it.
Yes, I believe it was from his final season when he was an All Star for the 1962 expansion New York Mets that won only 40 games. YLT frontman Ira Kaplan was born in 1957 so that might have been the first baseball team he followed.