How does SSL Proxy server in company work?

I've never seen SSL warning in company

Did you verify that SSL interception is done at all? See How do I check that I have a direct SSL connection to a website?.

So how does they intercept trafic without browser warning?

A SSL intercepting proxy creates a SSL connection between the proxy and the original target server and another SSL connection between the proxy and the client. The latter connection will use a certificate signed by the proxy CA. Insofar it is a classic SSL man in the middle attack and the only difference between the attack and the "legal" interception is that the client system has explicitly trusted the proxy CA and thus it will also trust the certificates signed with the proxy CA.

I doubt that they install trusted certificates from their proxy into the OS (because browsers may use different certificates store, Firefox has it's own for example).

If you have different CA stores for the different browsers you would need to import the proxy CA into all of these.

If a host wants to go to "https://google.com", the hostname into the certificate will be that of the proxy , not google

No. The subject of the certificate will be the original hostname (i.e. google.com). But this certificate will be signed by the proxy CA and not the original CA. And since the client trusts the proxy CA and the hostname matches the certificate no warnings will occur.