The halachah is in accordance with Tosfos (Rema 42:4). Therefore, there is no need to designate eidim, and even those who did not intend to testify may serve as the eidim (Shulchan Aruch, Choshen Mishpot 36:1; Pischei Teshuvah, Even HaEzer 42:11). However, a number of Achronim (see, for example Radvaz, 2:707; Shach, Choshen Mishpat 36:8; Beis Meir 42:2; Ketzos HaChoshen 36:1) record that it is customary to designate the eidei kiddushin. The Aruch HaShulchan (Even HaEzer 42:31), for example, writes:
It is proper to designate the witnesses for the kiddushin under the chuppah, and it is customary to do so in many holy communities, and it is proper for a number of reasons. First, as those who are at the wedding ceremony are often distracted by the wedding music and they do not witness the actual kiddushin, [witnesses are designated] in order that two witnesses should see the kiddushin. Second, since those standing under the chuppah who see the kiddushin are generally related to each other, and those who are valid eidim generally stand far from the chuppah and do not at all see the kiddushin... therefore, it is proper for the chosson to designate the witnesses. However, in order to spare him this embarrassment and responsibility, it is proper for the officiating rabbi to designate the eidim.
If the eidim were not designated and other people witnessed the kiddushin ceremony, the wedding is still valid.
