The golf term for the area of grass surrounding the putting surface is the apron.
The apron is a closely mown transition zone between the putting green and the fairway or rough. Its grass is usually longer than the putting surface but shorter and smoother than nearby rough, allowing a ball to roll more predictably than it would from thicker grass. On many courses, the apron is most noticeable in front of the green, where the fairway approaches the putting surface.
Golfers may choose to putt from the apron, chip the ball, or play a bump-and-run shot. The best choice depends on the grass height, slope, moisture, and distance to the hole. A common mix-up is calling every surrounding strip the “green”; under the Rules of Golf, the putting green is the specially prepared surface, while the apron remains part of the general area. “Fringe” and “collar” are related terms and are sometimes used interchangeably, although course-maintenance specialists may distinguish them.