The common US nickname for a highway lane reserved for carpools and marked with a diamond is “diamond lane.”
The name comes directly from the white diamond pavement symbol used to identify lanes reserved for high-occupancy vehicles, or HOVs. These lanes typically require a driver to carry at least one passenger, though the minimum occupancy can be two or three people depending on the roadway and time of day. Some systems also permit buses, motorcycles, or qualifying low-emission vehicles.
“Carpool lane” and “HOV lane” are often more precise everyday terms, while “diamond lane” emphasizes the road marking. A diamond lane does not necessarily mean traffic will move faster: congestion, enforcement, reversible operation, and access restrictions all affect its performance.
The diamond symbol can also identify other special-purpose lanes in some places, including bus or bicycle facilities. In the US highway context described here, however, it is strongly associated with a carpool or HOV lane.