In Parshat Lech Lecha, as Avram's mission in life changes from Father of Aram (who taught G-d's existence to the people of his native land, Aram) to Father of a Multitude of Nations, Hashem changes his name to Avraham. Hashem takes a "HEI" from His own Name and adds it to the name of Avram.
Then he changes the name of Avraham's wife as well. "As for Sarai your wife - do not call her name Sarai, for Sarah is her name." (Bereishit 17:15)
Why did Hashem change Sarai's name? She already had a "YUD" from G-d's Name incorporated into her own name.
And that is precisely the point. Hashem created a balanced world. In fact, we even learn that on Rosh Hashana, we are to think, "The scales are exactly even and I must do yet another good deed to tip the scales to the positive."
The world is balance. There was prophecy on one side of the scale and avoda zara (idol worship) on the other side. There was Israel on one side and Rome on the other.
Hashem built the world like a mathematics equation that is perfectly balanced.
So, G-d took a "hei" (equivalent in gematria to 5) and added it to Avram's name. Yes, it is a letter of G-d's Name, but the letter wasn't taken from there, because the "hei" still is found in G-d's Name. Where did He get the "hei" from?
From Sarai's name!!! - a name already containing a "yud", a letter from G-d's name. Sin, Raish, Yud. The letter "yud" is equivalent to 10 in gematria.
Hashem took the "yud" - 10 in Sarai's name and split it in half, sharing it between husband and wife. "Hei", five for Avraham and now five for Sarah.
But nothing has changed. The ten still exists, because the "yud" of G-d's Name is now shared between Avraham and Sarah (husband and wife). And we know that ishto k'gufo, one's wife is like one's own self. (Tosfot, Gittin 45a). So, the ten has stayed with Avraham/Sarah - a perfect equation for a perfect couple.
This parsha thought is dedicated in honor of Harav Moshe Eliahu Katz upon his bar mitzvah anniversary. B"H we had the opportunity to enjoy this parsha's Shabbat together with Moshie and his family.