Jack Smith is referenced in a 2002 NY Times article for the Abner Louima trial, so if he changed his name, it was before 2002:

https://www.nytimes.com/2002/07/09/nyregion/schwarz-case-proves-guilt-us-contends.html

"In a closing statement to the jury yesterday, a prosecutor argued that a massive amount of evidence proved that Charles Schwarz, a twice-convicted former police officer, should be convicted again of assisting in the assault of Abner Louima five years ago and then lying about it at a trial two years ago.

That man right there, said the prosecutor, Jack Smith, pointing across the well of the courtroom at Mr. Schwarz, participated in the sodomy of another man with a broomstick while he was a New York police officer."

Here's a list of qualifications we can cross-reference against:

Smith began his career as an assistant district attorney with the New York County District Attorney’s Office in 1994.

He worked in the Eastern District of New York in 1999 as an assistant US attorney, where he prosecuted cases including civil rights violations and police officers murdered by gangs, according to the Justice Department.

As a prosecutor in Brooklyn, New York, one of Smith’s biggest and most high-profile cases was prosecuting gang member Ronell Wilson for the murder of two New York City police department detectives during an undercover gun operation in Staten Island.