How to add a second site name to the index?

Question

Search Engine Optimization

Hello!
Please tell me how you can tell search robots that the site has a second name by which users can search for it?
There is an online store with a name that echoes an existing dialect (for example, akkuratno.com.ua (all matches with existing stores are random :) ))
At the moment, it is in the search results for "akkuratno", "akkuratno com ua" , but missing for the queries "neatly", "neatly com ua".
How to index these titles?
At the moment, I added alternative names to the keywords meta tag of the main page, but the situation has not changed in 2 months.
Also, I tried to put appropriate anchors on external links, but the idea did not take off either.
At the moment, we are not talking about reaching the top, it is important to simply index the names in Russian :)

Answer 1

If I understand correctly, then you want your site to become vital on the second request.
Those. displayed with a beautiful snippet in the first position.
If this is the case, then in the example above, you will not be able to appear on the request "neatly", because request is very general. And according to "neatly com yua" it may well appear. Check the occurrences on the page. Keywords will not help here, we need text entries on the page.

Answer 2

What for? Are there many such requests in Wordstat or just a whim?