Appears to have been created as a name variant on Ashfield, originally a house name and applied to several streets in the same neighbourhood. As far as we are aware, there is no evidence for a house or other place called Ashdene apart from Ashdene Drive.
See Ashfield Court / Crescent / Drive / Gardens.
"On the application of Messrs. F. B. McKee & Co. Ltd., 9 Shore Road, it was Resolved - That the name Ashdene Drive be approved for a new street on Messrs. McKee's property, situate off Glandore Avenue". (3rd April 1928).