Yes. One place to see this is Romans 3:23-25. "All have sinned and fall short of the glory of God." Notice that sin is defined in relation to the glory of God. Sin belittles the glory of God. It makes God look less valuable by desiring something else more. Then Paul describes God's remedy for that derision of his glory. Verse 24: ". . . and [they] are justified by his grace as a gift, through the redemption that is in Christ Jesus, 25 whom God put forward as a propitiation by his blood, to be received by faith. This was to show God's righteousness, because in his divine forbearance he had passed over former sins."
What we see here is that God sent Jesus to die ("by his blood"), and that by dying the righteousness of God could be vindicated and his anger could be propitiated and sinners who had belittled God's glory could be justified by faith alone. Why did God's righteousness need to be vindicated in this way? Because (v. 25b) he had passed over sins. That is, he had acted as though the derision of his glory didn't matter, and thus his righteousness, his allegiance to that glory, is called into question. He acted as though his glory was of little worth. But it is of infinite worth. And God would be untrue, he would be unrighteous, not to uphold and display the true value of his glory. Therefore, in order to justify sinners (like us!) who belittle his glory, and yet not himself belittle his own glory (in acting as though it didn't matter), he shows the infinite value of his glory by vindicating it with the death of his own Son who died for his Father's glory (John 12:27-28).
Therefore, what Romans 3:23-25 shows (as well as 3:1-8 and other places) is that God's righteousness is, at its essence, God's unswerving allegiance to the infinite value of his own glory - his own name. It's his unwavering commitment to uphold and display his glory and his name.