My family always called it the “parking strip”, and I had no idea until this day that it wasn’t a universal term.
It’s a Devil Strip dang it. I mowed grass in Akron for 5 or 6 years and it was always a Devil Strip. I can’t imagine not having a name for it. It was one of the most commonly used work phrases while I was there. Such as “You mow the devil strip while I weedwhack the backyard.” I was baffled by the use of “treelawn” when I moved to Cleveland.
stomps off to get a Galleyboy
double post.
Add me to the “I have no word for this” list.
ETA: but I’m glad I’ll now know what the heck someone else means!
I was going to wade in to vote for “treelawn”, but apparently we Cleveland natives are already well represented herein… 
I’m another “berm”-er here in New York.
Civil Engineer. Public Works.
According to the City of Stockton’s Standard Specifications, it’s a Parkway. Of course that only matters in Stockton. The City does not presume to name things outside of the City. If it’s a smaller, square opening, it’s a tree well. There are different sidewalk/street cross sections for different types of street (see Standard Drawings 11A through 11H).
The City Right of Way (ROW) usually extends about 3 ft. behind the back of the sidewalk. That’s also the preferred location of the Public Utilities Easement (PUE). Lots of people install fences, trees, bushes and/or hedges right against the back of the walk without checking to see where their ROW ends. If any construction is needed in the ROW, they get a rude surprise.
If you’re installing any of the above, I’d recommend calling the Permit Center (or your local equivalent) and asking where your ROW ends. They’ll recommend that you get it surveyed, but if pressed will mention that it looks like it’s about X feet from the back of the walk, the back of the curb, or the center of the street, depending on when your street was developed and what landmarks are available. It might even be at the back of the walk. It usually isn’t, but there are a few streets where it is.
Now I’m going to think “Verge escapement” whenever someone farts. Thanks, Rayne Man. (That’s not sarcasm, by the way. I’ve written two different limericks about my youngest son’s farts.)
We call it the “lawn extension”, but that seems to be very local. Googling “lawn extension”, the top relevent hits are all from Washtenaw county, MI.