I have changed my blogger domain name. The old address is still showing for online searches. Will this revert to my new domain address over time?
Yes, it will - eventually, as Google gets around to indexing your new site, and de-indexing your old one. It may take quite a while though.
If your old domain name was a custom one, then you may be able to use redirection features provided by the domain-name provider to redirect visitors to the new domain. Although this isn't available if you purchased the domain from Google via Blogger.