The main lawyers arguing the birthright citizenship case are the Trump administration’s solicitor general team on one side and lawyers for the challengers, including the ACLU, on the other. In the ACLU’s live coverage, National Legal Director Cecillia Wang is identified as arguing for the challengers, and SCOTUSblog says the case is Trump v. Barbara.

Who’s on the court side

The Supreme Court heard arguments on the Trump administration’s executive order seeking to end birthright citizenship for children born in the U.S. to people in the country illegally or temporarily. Reporting on the hearing says the administration’s position is that “subject to the jurisdiction” should be read narrowly, while challengers argue the 14th Amendment protects birthright citizenship as traditionally understood.

If you meant the individual lawyers

Publicly identified by the sources I found, Cecillia Wang of the ACLU was arguing for the challengers. The government’s specific courtroom advocate was not named in the source snippets I could verify here, but the case is being argued for the Trump administration by the government’s legal team.

Quick note

If you want, I can also give you the exact names of the lawyers on both sides in a simple two-column table.