Nys State income tax for out of state resident?

I own a single member llc that is registered in NY. I am a therapist and see all clients via telegraph remotely (this is my income source). Patients are mostly located in NY. In August, I moved to Washington State and no longer come to NY for any physical business purposes. My questions are: 1. Am I still obligated to pay nys income tax on clients that still reside in NY? (My previous clients still live in NY) 2. Because my llc is registered in NY, does this obligate me to pay any specific NY taxes even after I have moved? 3. Should I register a new llc in the state of Washington?