Yes Ural is unusual but not U.S. or U Morgan or men with U as middle initial. Any one of them could be a 'Ural' in SSDI or other records. There is a Ural Morgan b. 1911 which could be the RR worker. So if 'your' Ural enlisted before 1943 you should have where he was in August 42 to May 43 if you get service records. Track down all you can on your Ural before you look for a possible daughter in CA. Divides your attention.
Ural Standford Morgan could have been released from the Navy after the war in CA and applied to SSA for number to get a job right away. That is what my husband did while he waited to get out while at Terminal Island CA. He was there for 3 months and had his number before he left the service 1946.
Rootsweb.com's SSDI has a link to a copy of SS-5 letter and it will be $29.00 for a photocopy mailed to you or you can go to SSA wesbsite and get an "computer extracted" one for $16.00. http://www.ssa.gov/foia/html/foia_guide.htmhttp://www.ssa.gov/foia/html/foia_guide.htm It will give you the date he applied and any occupation (if any) he had and his address, as well as parents names. That information should help in deciding if the female born 1943 could be your Ural's daughter.