It is likely Wyndham Street was named after the politician George Wyndham who in November 1900 became chief secretary for Ireland. Even after leaving Ithe post, he kept a keen interest in Irish affairs.
"That on the application of the owner, Mr. R. J. Martin, 7 Wellington Place, a new street on his property situate off Elmwood Street be named Wyndham Street". (23rd September 1902).