This article is an excerpt from our Sefer
Buy me on Amazon.com
When is the Bris to be performed on Purim, before or after the Megillah reading? Some Poskim rule one is to perform the Bris and then read the Megillah. Others rule one is to read the Megillah [and complete the Davening] and then perform the Bris. Practically the custom is to perform the Mila and then read the Megillah. If however the Bris is not taking place in Shul then it is to be performed after the Davening is complete.
May a delayed Bris [passed the 8th day] be set for Purim?
What name should be given to a child born or circumcised on Purim?
It is customary to call a boy by the name Mordechai and a girl by the name Esther or Hadassah.
 Rama 693/4; M”B 696/29 based on Rama 696/8
 The reason: As these matters do not involve joy to the point we forbid allowing it to coincide with the joy of Purim. [M”B 696/29]
 Piskeiy Teshuvos 696/13
 Rama 693/4; Terumas Hadeshen 266 [regarding if there is time to do both, brought in M”A 687/5]
 The reason: The reason for this is because in the Megillah the verse states “Layehudim Haysa Orah Vesimcha Vesason” and Sason is Milah. As well in order to be a Jew which celebrates Purim one must first perform the Mila. [Darkei Moshe 693/4; Mateh Moshe 1020; Drashos Mahril Purim; M”A 693/3; M”B 693/11]
 M”A 687/5; Opinion in Terumas Hadeshen 266; Peri Chadash; Biur Hagr”a; Beis Yosef Yoreh Deah 262 in name of Orchos Chaim; Ridbaz 1/251; Kneses Hagedola 687; Implication of Michaber 687/2; Yifei Laleiv 2/10; Peri Megadim; M”B 687/9; 693/12; See Kaf Hachaim 687/15; 693/30
The reason: As the Mitzvah of Megillah contains Pirsumei Nissa and hence pushes off the Mitzvah of Mila. [ibid]
The law if there is only enough time to either read Megillah or perform the Bris? This matter is disputed in Poskim. The Terumas Hadeshen ibid rules that one is to precede Megillah. Other Poskim however rule one is to precede the Bris. Practically if the Bris is on the eighth day then in such a case one is to perform the Bris and push off the Megillah reading. [P”M 687 A”A 5]
 Chayeh Adam 154/6 brought in M”B 687/9; Siddur Yaavetz; Piskeiy Teshuvos 694/8; Luach Kolel Chabad; However see Hiskashrus 1025 footnote 54 that writes one is to do the Bris after the reading, and that so was the custom of the Mohel Yaakov Yosef Raskin.
Custom of Sefaradim: See Yalkut Yosef 317 that the custom of Sefaradic Jewry is to perform the Bris after the reading. See Kaf Hachaim ibid who rules likewise.
 Aruch Hashulchan 694/5
 Piskeiy Teshuvos 696/13
 Otzer Habris 1/182 in name of Tashbatz 3/8; Yosef Ometz [Kadmon] 1098. [I have not found this mentioned in these sources]