Albert Barnes Commentary Psalms 76:1

"In Judah is God known: His name is great in Israel." — Psalms 76:1 (ASV)

In Judah is God known – That is, He has made Himself known there in a special manner; He has demonstrated His watchful care over the city, so as to demand proper acknowledgment; He has manifested Himself there as He has not elsewhere. It is true that God is known, or makes Himself known, everywhere; but it is also true that He does this in some places, and at some times, in a more marked and striking manner than He does in other places and at other times. The most clear and impressive displays of His character are among His own people - in the church. His name is great in Israel. Among the people of Israel; or, among His own people.

The meaning here is that, by some act referred to in the psalm, He had so displayed His power and His mercy in favor of that people, as to make it proper that His name should be exalted or praised.