- The Matteh Moshe (a student of the Maharsha"l) writes that we wait until just after the Brit Milah to give a baby boy his name because Avraham Avinu received his name (Avraham) after performing his Brit.
- After Avraham Avinu performed his Brit Milah, the Torah tells us that Hashem gave him the entire land of Eretz Yisrael. I have seen written in the name of Rav Yaakov Emden that our common practice of giving a gift to the baalei simcha at a Brit has its source in this gift that Hashem gave to Avraham. When we give a gift to the ba'alei simcha, we are mimicking the actions of Hashem who was the first to bring his gift to the very first Brit.
I have not yet found this R' Yaakov Emden in writing... but when I do I will let you know where you can find it.
Shabbat Shalom