My old passport under my nickname with US Visa in it was declared lost or stolen So I wasn’t able to leave. US authorities asked me to get a new passport. Now i have my new passport with my name in my birth certificate. Can I still travel to the USA?
You will need a new visa and need proof that you lost your old passport and visa.
From the gov website:
Lost or stolen U.S. visas cannot be replaced in the United States. For replacement of a visa, you must apply in person at a U.S. Embassy or Consulate abroad. When applying for the replacement of a visa, you will need to provide a written account documenting the loss of your passport and visa.