Two domains, is it possible to do this?

Question

Search Engine Optimization

There is a site that is well indexed in the search. During the transition. I immediately redirect to the new domain. 301 redirect.
Site1.rf and when I go to any page from the search, I change it to
Site1.ru
But I want it to stay that way. In the index, let there always be site1
But in the browser I want it to be site1.ru
Or because of a 301 redirect, then site1 will take place in Google?
How to do what I want?
Tk for displaying information, I want to change domains so that they are foreign or such so as not to dig in.