According to MIT legend, the bridge is so named, despite the fact that it is nearer to MIT than to Harvard (and is also known informally around Boston as the "MIT bridge"), because when it was originally constructed, the state offered to name it after the Cambridge school that was most deserving. Harvard argued that their contribution to education was well-known, and thus they deserved the name. MIT concurred, having analyzed the bridge and found it structurally unsound, and thus more deserving of the Harvard name than the MIT name. Subsequently the bridge was rebuilt, confirming the MIT engineer's fears.
The story is aprocyphal. The real reason for the name is that Harvard Bridge was first constructed in 1891, while MIT only moved to its current location in 1916. Nevertheless, the bridge was rebuilt in the late 1980s to convert it to a more modern four-lane highway.