I did my best to list the people that streets are named after. As you approach the end of the 19th Century, it gets harder to figure out who the streets are named for - I'm guessing that most of them were not long-time residents. Thus, no Sheridan, no Hall, no Dunster or Dane streets. No doubt I've missed some easy ones. Unfortunately, no one kept records of who named the streets, or how the names were chosen.
Achorn circle - Edgar Achorn, lawyer, lived along South st.
Amory st - Amory estate.
Ballard st - Ballard family owned land along South st.
Beethoven st - German composer.
Bismark st - German politician.
Boylston st - Nicholas Ward Boylston, owned land from Centre street back to the railroad tracks.
Brewer st - Sarah Brewer lived in the house at the corner of Brewer and Thomas streets.
Brown terrace - land owned by A.S. Brown, businessman.
Burroughs st - William Burroughs laid out road.
Bussey st - Benjamin Bussey - owner of the Arboretum land during early 1800s.
Call st - John M. Call had an estate near Green street train station.
Child st - probably Abner Child - owned land across South street - sold the land for St Thomas' church.
Eliot st - John Eliot, Apostle to the Indians, gave the land on either side for the Eliot School.
Goldsmith place - Benjamin Goldsmith owned a house along Centre st and a slaughterhouse set
back from the road.
Goldsmith st - Benjamin Goldsmith owned a farm along Centre street where the Arborway and the Arboretum are now.
Goodrich rd - Samuel Goodrich, pen name Peter Parley, lived across Centre st.
Greenough ave - D.S. Greenough developed the street from his family's estate.
Hagar st - Daniel Hagar was principal of the Eliot school during the mid-1800s, lived in the area.
Harris ave - Luther Harris, doctor.
Heath st - Heath family, including General Heath, Revolutionary war.
Holbrook st - Amos Holbrook had a house and farm along Centre st beside the Unitarian church.
Hopkins Road - named in 1926 for Sabina Hopkins McCourt, mother of Francis M. McCourt (1886-1956) who purchased and developed the street and surrounding lots (added from comments).
John A. Andrews - Mass. Civil War Governor
Lamartine st - French poet, friend of Samuel Goodrich, whose estate was part of Lamartine street.
Louder's lane - Louder family.
Marlou terrace. - A portmanteau name from Marie and Louis Mahn, owners of the land later subdivided into the street.
May st - May family - John May, settled the land in the 1600s.
McBride st - deceased WW I soldier
Meehan st - Patrick Meehan, builder, developer owned land.
Mozart st - Austrian [German] composer. Commenter Eeka points out that Mozart was Austrian. The Germans of Jamaica Plain may have seen him as one of their own.
Newsome park - George Newsome bought estate, moved the old house and developed the street.
Parley ave - Author Samuel Goodrich had estate on site.
Parley vale - Same as above.
Paul Gore st - Gore family owned land along Centre street at site of road.
Perkins st - James Perkins purchased Pinebank land in early 1800s along Connecticut road,
named Perkins street in 1825.
Peter Parley rd - Pseudonym of author Samuel Goodrich - built a house here, but never lived in it.
Prince st - Capt.John Prince bought the old Governor Bernard estate along Jamaica Pond, developed the road between Pond and Perkins streets.
School st - land surrounding School st between Stony brook and Walnut avenue was donated to the Roxbury public school - later Roxbury Latin - by Daniel Bell.
Seaverns ave - Luther Seaverns owned land the fronted on Centre street where Seaverns ave. is now.
Starr lane - Daniel Starr, blacksmith, had a shop set back from Centre street here during the early 1800s. Starr lane was probably a right-of-way to get to his property. His wife actually bought the land in her own right.
Thomas st - Hugh Thomas and wife donated land to the Eliot School.
Walter st - Rev Walter, first pastor of 2nd Roxbury parish.
Warren sq - land formerly owned by Dr John Warren.
Weld avenue - Weld family owned Arboretum land until 1802, and much of Forest Hills after that.
Weld Hill st - Weld family.
Wyman st - Wyman family owned land here.