Psalm 135:13, "Your name, Yahweh, endures forever; your renown, Yahweh, throughout all generations," is a powerful statement about the eternal nature and enduring reputation of God. Let's break it down:

"Your name, Yahweh, endures forever": The name "Yahweh" (often rendered as LORD in English translations) is the personal name of God in the Hebrew Bible. It's not just a label; it represents God's essence, character, and attributes. To say that the name "Yahweh" endures forever means that God's very being, his eternal existence, his inherent nature, will last for all time. God is not temporary or fleeting; He is permanent and unchanging.
"Your renown, Yahweh, throughout all generations": "Renown" refers to God's reputation, fame, glory, and how He is known and perceived. The second part of the verse emphasizes that God's reputation will be known, respected, and acknowledged "throughout all generations." This means that in every time period, among all peoples, God's mighty deeds, His faithfulness, His justice, and His love will be remembered and proclaimed.
Essentially, the verse is saying:

God's essential nature (His name, Yahweh) is eternal and unchanging.
God's reputation (His renown) will be known and celebrated by people in every generation.

The verse is a declaration of faith that affirms:

God's permanence: In a world of constant change and uncertainty, God remains a constant presence.
God's faithfulness: Because God's name and renown endure, believers can trust in His promises and rely on His character.
God's enduring impact: God's actions in history and His relationship with His people will continue to resonate and inspire future generations.

This verse is often used in worship and praise as a reminder of God's eternal nature and His unwavering commitment to His people. It is a call to remember God's faithfulness and to proclaim His glory to all the world.