Jessica Alba might name her baby Honor

Actress Jessica Alba accepts the award for Favourite Movie Actress at the Nickelodeon's Kids' Choice Awards in Los Angeles March 29, 2008. [Agencies]

Actress Jessica Alba, who is expecting her first child with fiance Cash Warren, might name her baby daughter Honor.

Alba has still not made the baby's name and sex public, but her friends have already started speculating, contactmusic.com reports.

One of her friends revealed a little too much when she went shopping for a baby shower gift at a Los Angeles boutique. 'This woman was so exited that Jessica is having a girl,' said a source.

Another family friend picked out a charm bracelet for the unborn baby that spelled out 'Honor'.

Alba's manager Chris Henze's wife is throwing the baby shower in Los Angeles this coming weekend.