Google always shows the actual URL for your site and never uses alternate domains.
If you want to show your custom domain in the Google Search results, you have to use that domain for your site. WordPress.com has instructions for doing so here. The basic steps are:
- Register the domain
- Add the domain to your wordpress.com account
- Point or transfer the domain to wordpress.com for hosting
- Set the domain as the primary domain for your account
That last step requires that you pay for wordpress.com hosting. There doesn’t appear to be a way to use a free wordpress.com account with a custom domain set as the primary.