Answer by taking a quote from the following article:

The New York Dolls were an American hard rock band formed in New York City in 1971. Along with the Velvet Underground and the Stooges, they were one of the first bands of the early punk rock scenes. Although their original line-up fell apart quickly, the band's first two albums--New York Dolls (1973) and Too Much Too Soon (1974)--became among the most popular cult records in rock.

Sylvain Sylvain and Billy Murcia, who went to junior high school and high school together, started playing in a band called "the Pox" in 1967. After the frontman quit, Murcia and Sylvain started a clothing business called Truth and Soul and Sylvain took a job at A Different Drummer, a men's boutique that was across the street from the New York Doll Hospital, a doll repair shop. Sylvain said that the shop inspired the name for their future band. In 1970 they formed a band again and recruited Johnny Thunders to join on bass, though Sylvain ended up teaching him to play guitar. They called themselves the Dolls. When Sylvain left the band to spend a few months in London, Thunders and Murcia went their separate ways.  Thunders was eventually recruited by Kane and Rick Rivets, who had been playing together in the Bronx. At Thunders' suggestion, Murcia replaced the original drummer. Thunders played lead guitar and sang for the band Actress. An October 1971 rehearsal tape recorded by Rivets was released as Dawn of the Dolls. When Thunders decided that he no longer wanted to be the front man, David Johansen joined the band. Initially, the group was composed of singer David Johansen, guitarists Johnny Thunders and Rick Rivets (who was replaced by Sylvain Sylvain after a few months), bass guitarist Arthur "Killer" Kane and drummer Billy Murcia.  The original lineup's first performance was on Christmas Eve 1971 at a homeless shelter, the Endicott Hotel. After getting a manager and attracting some music industry interest, the New York Dolls got a break when Rod Stewart invited them to open for him at a London concert.

How did "the Pox" evolve into the New York Dolls?
In 1970 they formed a band again and recruited Johnny Thunders to join on bass, though Sylvain ended up teaching him to play guitar.