Oscar is Rudyard Shelton's grandfather. His son John Shelton chose Rudyard's middle name, Oscar, after him. (Ask the Characters) When an anti-matter duplicate of Shelton was created during the bridge accident, it chose to go by Shelton's middle name and was also called Oscar Shelton.
In September 2022, Shelton refers to his duplicate as "the only other member of his family" alive, meaning his grandfather probably had died by this point. (Shelton's Last Day)