My website comes up #2 on a search, however it is showing my old URL, how do I get it

My website comes up #2 on a search, however it is showing my old URL, how do I get it changed to my new URL?


When I type in "Amsoil Columbus" my site shows at #2, however the URL is bestsynlubes.com (which was my old URL and has since been changed) my new URL is HighTechSyntheticOil. com and I would like it to appear when anyone searches this term. I do have a re-direct going to my new site, but I am trying to eliminate all references to my old URL.


What do I need to do??