Yes: the first English settlers in Hartford called the hill Lord's Hill after the English family that owned the land here. This name persisted throughout the 19th century and even into the 20th century before falling out of use. We don't know why it did fall out of use, but the timing seems to coincide with the death of the last Lord descendant to live on the hill. Prior to Lord's Hill, there are several Hartford histories that claim the local Algonquins called the hill Watch Hill, because they used the hill as a lookout. It should also be noted that our friends at the American School for the Deaf have told us that the deaf community has long opposed the name Asylum Hill and that the students mounted several efforts to change the name to something else.
Asylum Hill is named for the Asylum for the Deaf and Dumb, now the American School for the Deaf, which located itself on the Hill in 1818. It's not clear how quickly the name of the neighborhood changed to reflect the school's presence here, but it seems to have happened pretty quickly.