Here is Gregory Peck's listing in the Social Security Death Index (SSDI):
GREGORY PECK
Birth: 05 Apr 1916
Death: 12 Jun 2003 (V)
Last Residence: 90077 (Los Angeles, Los Angeles, CA)
Last Benefit: (none specified)
Social Security Number: 547-16-9811
Issued: California
Using the information from an SSDI listing, a copy of the person's SS-5 form can be obtained from the Social Security Administration for a fee. The SS-5 is the form a person filled out when they applied for a Social Security Card. Here's a copy of Gregory Peck's SS-5 (click on it to see a larger view).
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As you can see it gives all sorts of information about the person that can be useful for further genealogy research. The SS-5 for Gregory Peck shows his full name (Eldred Gregory Peck), his date and place of birth (April 5, 1916 in San Diego, California), and the full names of his parents (Gregory Pearl Peck and Bernice Mae Ayres). Note that the maiden name of his mother is given. (There are restrictions regarding the release of the parents' names -- see the link below.) This SS-5 also shows the name and location of his employer, and his address in San Diego when he applied for his Social Security Card in 1937, which is about 6 years before he made his first film.
While putting this article together I asked my mother what her favorite Gregory Peck movies were. Here is her list: Keys of the Kingdom (1944, his second film), Duel in the Sun (1946), Gentleman's Agreement (1947), Twelve O'Clock High (1949), Roman Holiday (1953, with the great Audrey Hepburn, who became a lifelong friend), and To Kill a Mockingbird (1962). During his film career he received five best actor Academy Award nominations, and won the Oscar just once. That was for To Kill a Mockingbird. I think it's fitting that he will likely be remembered for the role of Atticus Finch. Gregory Peck may have died in 2003, but thanks to him and Harper Lee, Atticus Finch will live on in the film and novel.
Helpful Links
Social Security Death Index - Online Searching
How to order a copy of the Application for a Social Security Card (Form SS-5) of a deceased person Note the restrictions given there regarding proof of death and the release of parents' names.