When the dominant culture succeeds in imposing its values and ideas on all of society, it is known as:?

This is known as hegemony.

The word hegemony comes from Greek word hegemon, which means leader. So, when English language took this word from Greek and incorporated it into its own language, it got the meaning of dominance, dominion, leadership, etc. So if one country dominates over another one, this is known as hegemony.