Yes in theory although New York State may reject the other names. You probably won’t run into a problem if the LLCs are in different industries and the names vary to some degree. An alternative to forming multiple LLCs would be to set up multiple DBAs (“Doing Business As”) under one LLC.
If you’d like to discuss your options with a startup attorney, or want to form your LLC then I invite you to. Our rates are a fraction of what you’ll pay through the traditional law firm experience, and we offer free no obligation price quotes. Good luck!