How does a sleep doctor distinguish between persistent sleepiness even after cpap use and narcolepsy?

By taking a history: ...And reviewing the results of your sleep test. There are specific findings on a sleep test, and a multiple sleep latency test, than can fairly easily distinguish among the options you refer to.

Doing further "sleep: If one has a normal sleep study with the use of c-pap, one can do testing during the day to determine how fast the patient falls asleep in a darkened room and whether the subject enters rem sleep quickly. If this occurs, the subject probably has narcolepsy ( assuming the patient has further symptoms of the disorder).

MSLT: A multiple sleep latency test can be performed which in combination with some genetic studies may help separate narcolepsy from excessive somnolence due to obstructive sleep apnea. Unfortunately even well treated sleep apnea can result in daytime somnolence. There are medications which may help this.

MSLT: A multiple sleep latency test could be performed after CPAP use if a patient were still persistently sleepy. This would help to differentiate hypersomnia vs narcolepsy.