Milah removes the covering that conceals holiness

זכרתי לך חסד נעוריך כו' לכתך אחרי כו' הוא רמז על אאע"ה שעזב בית אביו ומולדתו וזה הכח נשאר קיים בבנ"י:

"I remember for you the kindness of your youth… your following after Me…" (Yirmiyahu 2:2) — this alludes to Avraham Avinu, who left his father's house and his birthplace, and this power remained enduring within Bnei Yisrael.

The verse about Israel's youthful devotion hints at Avraham's act of leaving everything to follow Hashem; that very strength of self-uprooting was implanted permanently in his descendants.

בענין המילה דכ' במד' תנחומא שע"י המילה נעשה תמים אף שלעיני בשר הוא עוד מחסר מבשרו.

Regarding milah: it is written in the Midrash Tanchuma that through milah one becomes "tamim" (whole/perfect), even though to physical eyes he is lessening his flesh.

Strikingly, the Midrash says circumcision makes a person "complete" — even though physically it appears to remove and diminish part of him.

אבל הענין הוא כי מאחר שמצוה להסיר הערלה בודאי אין החיות הפנימיות והקדושה מתפשט בזו הערלה וכל שיש איזה מקום טימטום באדם שאין החיות מתעורר שם נק' חסר לכן ע"י מילה נקרא תמים.

But the idea is that since it is a mitzvah to remove the orlah (foreskin), surely the inner life-force and holiness does not extend into this orlah; and wherever there is some place of dullness (timtum) in a person, where the life-force is not aroused, that is called "lacking." Therefore through milah he is called "tamim."

The orlah is a place the inner chiyus (life-force) and kedushah cannot reach — a spot of spiritual numbness. Any such deadened place is a true "lack," so removing it through milah is what actually makes a person whole.

האדם הוא רמז לכל הבריאה שנק' עולם קטן וכמו שיש ערלה באדם כן בכל דבר צריכין להסיר המכסה והערלה.

Man is an allusion to all of creation, for he is called a "small world" (olam katan); and just as there is an orlah in man, so too in everything one must remove the covering and the orlah.

Since the human being is a microcosm of all creation, the principle of milah applies everywhere: every thing has a "covering" that conceals its inner holiness and must be removed.

ובדורות ג"כ הי' דור המבול הערלה לכן נאבדו ונתגלה אח"כ נח הצדיק תמים.

And in the [course of the] generations too, the generation of the Flood was the orlah; therefore they were destroyed, and afterward Noach the righteous, "tamim" (perfect), was revealed.

On the scale of history, the corrupt generation of the Mabul was the "orlah" of the world; once it was removed, Noach — described as "tamim" — emerged as the world's purified core.

באברהם הי' התחדשות מאפילה לאור שמקודם הי' תהו כדאיתא במד'.

With Avraham there was a renewal from darkness to light, for beforehand there was tohu (chaos/void), as is brought in the Midrash.

Avraham brought a wholly new beginning, turning the prior chaos and darkness of the world into light.

לכן הוצרך לשנות שינוי מעשה במילה ושינוי מקום לך לך ושינוי השם:

Therefore he needed to make a change of deed — through milah; a change of place — "Lech lecha" (go forth); and a change of name.

Because Avraham's mission was a total renewal from darkness to light, it required three transformations: a change in action (milah), a change of place (his journey), and a change of name (Avram to Avraham).

Summary: Avraham's act of leaving everything to follow Hashem became an enduring power within Bnei Yisrael. Milah makes a person "whole" by removing the orlah — the place of spiritual deadness that the inner life-force cannot reach — and since man is a microcosm, every thing in creation has such a "covering" to be removed. So too the Flood was the world's orlah, cleared away to reveal Noach; and Avraham's renewal from darkness to light demanded three changes — of deed (milah), of place (Lech lecha), and of name.