01Short answer
Yes. Mamdani won office through Democratic Party elections in New York. He is also associated with the Working Families Party ecosystem and democratic socialist politics.
The DSA connection is political and organisational. It is not the same thing as being outside the Democratic ballot structure in New York City.
That combination is why voters see both labels: Democrat in electoral machinery, democratic socialist in ideology and organising.
02Why both labels appear
New York progressive politics often runs through overlapping institutions: Democratic primaries, the Working Families Party, unions, issue campaigns and DSA chapters.
Mamdani's campaign used Democratic primary rules and ranked choice voting while presenting a left affordability programme on rent, buses, childcare, wages and public ownership proposals.
03Governing test
The party label matters less than what passes. The record is budgets, appointments, board votes, state negotiations, agency operations and whether promises become services.