Albert Barnes Commentary Psalms 135:13

"Thy name, O Jehovah, [endureth] for ever; Thy memorial [name], O Jehovah, throughout all generations." — Psalms 135:13 (ASV)

Thy name, O Lord, endureth for ever - You are the ever-living, the unchanging God. The generations of people pass away; the kingdoms of the earth change; the idols perish, but You are the same.

The object here seems to be to bring the image or the idea of God before the mind as he was when he performed these great works, as a God interposing on behalf of his people, and as worthy of praise. The idea is that he is the same now that he was then. As he then impressed the world with a sense of his majesty and power, and as he then interposed on behalf of his people by mighty signs and wonders, we should feel that, being an unchangeable God, he can do it now, and is now equally worthy of confidence, adoration, and praise.

And thy memorial - Your remembrance; the memory of yourself. That is, what you have done to secure a remembrance among people is of such a nature as to make the same impression for all coming time. The events were such that the memory of them should never pass away from mankind.

Throughout all generations - Margin, as in Hebrew, To generation and generation. There never will be a generation on the earth, in the latest periods, to which the memory of these things should not be transmitted.