You're from Newton too, so you might know this:
Each of the names you listed actually was intended to represent a geographical location which would have been easily recognizable to people at the time the line was built. Riverside is named after the then-famous Riverside Recreation Area. The station was initially located at the junction between the B&A Circuit Line and the B&A Mainline, a spot now under the Turnpike (the junction is still there and is how DMUs on the Pike would access Riverside). The station is named after a place which no longer exists (attempts to rename the station either "Lower Falls" or "Auburndale" would slight one of those, and "Lasell" would piss off everybody).
Woodland was named after the Woodland Park Hotel. It's still there as the Woodland Golf Club's clubhouse. The original station (which is now a tool shed and is clearly visible from the Washington St. overpass) was meant to basically offer private access to wealthy hotel patrons. There simply isn't enough of a neighborhood around it to be called "Woodland," so perhaps "Newton-Wellesley Hospital" would be a better name these days. The apartment complex at the station does prominently display the name, however.
Eliot is the funny one, since it actually has no meaning at all, but was supposed to. The Eliot and Waban stations were both named by the same guy (Mark Strong, who owned the "Strong Block" in Waban Center). The new circuit line cut through a whole bunch of basically empty land, and the stations at Waban and Eliot initially served absolutely nothing. Strong named them after Chief Waban and John Eliot, two of his heroes and favorite characters from local mythology. As at Woodland, no discernible neighborhood ever grew around Eliot, so unlike Waban it means nothing today and really never has. (Side note - Chief Waban never lived anywhere near the village of Waban, and had no association with the location whatsoever). "Upper Falls" might make a better station name until GL to Needham happens.
