After setting up your custom domain,you must require a new sitemap for your domain.so submit a new sitemap to webmaster tool of Google, Bing/yahoo .
Change your blogspot.com name with your custom domain url at all social pages or profiles like Facebook,Twitter,Google+,stumble etc.
Submit your custom domain to all top blog directories.This will help you to increase back-links & page rank.
While commenting on any blog or in forums use your custom domain as your signature.This will help you to increase back-links
If you ensure that your custom url is perfectly working on blog than Go to alexa.com ,put your custom domain URL in box and hit enter.it will show your rank as "No Data". No Problem alexa rank will be cover in 1-2 weeks.it is only possible if your post frequency is one post daily.But before that put a alexa widget which contain your domain rank on your blog.it will help alexa to get your domain ranking early as possible.
Must Know :
After setting up custom domain on blog, it will effect your traffic and page rank.Because search engines will crawl your pages again that will take 2-3 weeks to complete indexing.