Parents of Chasan and Kallah share the same names:
If the parents of the Chasan and Kallah have the same exact name they should not have their children marry each other. This applies for the names of both the mother and the father. [However, some Poskim rule this only applies if the names of the fathers are identical, and not regarding the names of the mothers. Other Poskim rule the above only applies to small children, while children who are already adults may choose to marry someone even if their parents share names. Other Poskim rule the concern only applies if the parents share the same rare name, however by common names, such as Avraham and Yitzchak, no concern applies.]
A second name: If, one of the parents with the identical name has a second name which is not shared with the other parent, then there is no worry involved. [For example, if one is called Chaim Baruch, while the second is called Chaim, it is not a problem.] Likewise, even if the parents share the same exact name, if a second name is added to one of the parents, it suffices. Accordingly, if the mothers share the same name, then one of the mothers should have a name added.
If one of the parents has a nickname, or a secular name, are the names considered identical?
Seemingly, one may be lenient in this matter if the parent is called by this nickname or secular name.
 Tzavas Rebbe Yehuda Hachassid 24; See there that it is questionable whether this directive of Rebbe Yehuda was for everyone or only for his descendants, and hence we are only careful in this due to doubt [See Even Yikara Kama E.H. 15; Makor Chesed footnote 36]
 Sdei Chemed Asifas Dinim Mareches Chasan Vekala 10; Igros Kodesh 18/136
 Even Yikara Kama E.H. 15; Beis Naftali 12; Ruach Chaim E.H. p. 34; See Poskim in Sdei Chemed Asifas Dinim Mareches Chasan Vekala 10
 Avnei Tzedek E.H. 6 and 10
 Shem Mishimon E.H. 6
 Tzemach Tzedek Even Haezer 1/143; Piskei Dinim Y.D. 116; Igros Kodesh 18/136
 Igros Kodesh 18/136
 Igros Kodesh 18/136
 See Michaber E.H. 129 that a nickname or English name is considered a real name and must be written in the Get. See also Igros Kodesh 4/349 and Shulchan Menachem 6/140 that if he uses the similar name only for an Aliya and the like, then it falls under the allowance of the Tzemach Tzedek.