Police had withheld their names until they were identified by the Suffolk County medical examiner's office and the family was subsequently contacted.
The pair's 2006 Mustang hit a tree and burst into flames. The "resulting fire" meant "the identification process is not as immediate as normally experienced," a police spokesman said.
Police said the car was registered to Wheeler, but Cuhna was driving at the time of the crash.
Police said the accident was on Brick Kiln Road at about 3:34 p.m. They didn't say how fast the car was going.
Police said they are "awaiting additional reports from the medical examiner's office to ascertain if there are any other possible contributing factors," they said in a news release Tuesday.
Police ask anyone with more information to call the Southampton Town Police Detective Division at 631-728-5000, or the department's information hotline at 631-728-3454.