NASA's Perseverance Mars Rover

What are the current quadrants naming conventions or terrestrial region?

This map quadrant is called 'Gros Morne'

Gros Morne National Park is a Canadian national park and World Heritage Site located on the west coast of Newfoundland.

You can see all the original named quadrants on this map from early in the mission, I can't find a more recent one that identifies some quadrants outside the crater that the rover could visit.

This map shows various quadrant themes in the vicinity of NASA’s Perseverance Mars rover, each quadrant is 0.7 miles (1.2 kilometers) on each side.

The Perseverance team chose quadrant themes related to various national parks across Earth, from Shenandoah National Park in Virginia to Jotunheimen National Park in Norway. The themes help organize the unofficial nicknames that are given by rover team members to different surface features they want to study, such as hills, craters, boulders, and even specific rock surfaces. The first sedimentary rock core sample the rover took was from a rock nicknamed “Skinner Ridge” for a ridge in Shenandoah National Park when Perseverance was in that quadrant. Many hundreds of names are compiled into a list based on each theme and are applied as the rover explores that quadrant. Rovers can sometimes end up exploring a quadrant for months, exhausting the list of names and prompting a new list to be drawn up.