do i need to do anything further like get the old page removed from google's index? or will google update the link information when it indexes my new and current content?
Don't worry, it may take some time but it would be updated. Modify and resubmit your sitemap to Google. But if that listing is from DMOZ, you need to update those listings manually. Thankyou
Nothing you can do at the moment. Once the info has been changed, you just have to wait before google crawls your site and update it to their index.