If your site is accessible from more than 1 domain name, you have to redirect the old domain to the new one using 301 (Permanent) redirect.
Note: If you do not first set up 301-redirect directives, your change
of address request will not work.
Add and verify your new site with Search Console.
The first step in submitting a change of address request involves selecting your new site from a list, so make sure Search Console knows about your site.
Make sure you specify all relevant preferences for your new domain
that you set for your old site, including a preferred domain,
geographical preferences, and any crawl rate adjustments you might
There are few more steps you need to make before you change the address please read this article: https://support.google.com/webmasters/answer/83106?hl=en and make sure you got everything right, but 301 redirect from the old to the new domain are required before you throw googlebot in your new site, to avoid duplicate content flag.