What is your name?

There is certainly no shortage of מסכתות whose properly pronounced name is a matter of discussion. Is it Yuma or Yoma? Erchin or Arachin? I've even heard a suggestion that Yavmus is the proper pronunciation of what most of us know as Yevamos. But while those are more of a simple matter of word structure, the story behind how to pronounce our current מסכתא's name is quite a bit more rich. I searched around for some detailed write-up of the issue and found the following.
(Source: http://www.dafyomi.co.il/sanhedrin/insites/sn-dt-005.htm)

3) "BEITZAH" OR "BEI'A" OPINIONS: The Gemara relates that Rebbi visited a town and saw everyone kneading dough in impure vessels. When he inquired about their actions, the people of the town told him that "a certain Talmid told us that Mei Betza'im (water of swamps) does not have the ability to make a food susceptible to Tum'ah." They assumed, therefore, that since their dough was made with such water it could not become Tamei from their vessels. 

This was an outright mistake, as the Talmid actually had said "Mei Beitzim" (the liquid of eggs), and not "Mei Betza'im," swamp water. The people did not realize their mistake, and they even cited support for it from the Mishnah in Parah (8:10). The Mishnah there states that certain types of waters cannot be used for the Mei Chatas, the sprinkling of the ashes of the Parah Adumah, because they are swamp waters. They erroneously reasoned that the Mishnah there was the source for the Talmid's ruling: since such water is not usable for the Parah Adamah, it also must not be suitable to make something capable of becoming Tamei. As a result of that incident, the Chachamim decreed that a Talmid may not issue a ruling unless he has received permission from his Rebbi to do so. 

The Acharonim cite this Gemara when they discuss whether it is preferable to pronounce the word "Beitzah" (egg) as "Bei'a" (the Aramaic word for "egg"). 

(a) The MAGEN AVRAHAM (end of OC 156) in the name of the MAHARSHAL (Yam Shel Shlomo, Bava Kama 4:11) writes that "it is proper to say ['Bei'a' or] 'Bei'im' instead of ['Beitzah' or] Beitzim,' in order to maintain a high standard of purity of speech." (The word "Beitzah" is used by the Chachamim to connote part of the male reproductive system, and thus it is improper to utter it unnecessarily, as the Gemara in Pesachim (3a) teaches that one should accustom himself not to speak in an improper manner.) Based on this, many people have the custom to refer to Maseches Beitzah as "Bei'a," which is the Aramaic term for "egg." 

(b) The IYEI HA'YAM (cited by the Likutim on the Mishnayos), however, refutes this practice. He points out that there is no source anywhere in Shas that indicates that the Chachamim refrained from pronouncing the word as "Beitzah" or that they classified the word as improper speech. In fact, the Chachamim even used the word to describe many oblong objects (such as "Beitzas ha'Gir," Beitzah 15a). 

Furthermore, he argues, what does one gain by merely translating the Hebrew word to Aramaic if it has the same meaning in both languages? (See, however, BEIS EFRAIM, Teshuvos OC 15.) As clear proof that the word was pronounced "Beitzim" in the times of the Chachamim, he cites the Gemara here in Sanhedrin. Had the Talmid, when he referred to the liquid of eggs, not used the term "Betza'im" but rather "Bei'im," no mistake would have resulted. The townspeople would not have confused "Bei'im" with "Betza'im." (TOSFOS even has difficulty with how the townspeople confused the word "Beitzim" with "Betza'im." He explains that they thought that they heard the Talmid say "Bitzim" which they assumed was "Betza'im." Nonetheless, they would never have made this mistake had the Talmid said, "Bei'im.") 

(c) These arguments prompt the TIFERES YISRAEL (introduction to Beitzah) to suggest that the practice of not pronouncing the word as "Beitzah" is unrelated to concern for improper speech. Rather, he explains that since an error in Halachah was made because of the similarity between the words "Beitzim" and "Betza'im," the practice arose to pronounce the word "Bei'a" when used in a Halachic context in order to prevent such mistakes from happening again.
Nowadays, the generally-accepted practice is to pronounce the word "Beitzah," except in reference to the name of the Maseches, which some refer to as "Bei'a." Although the Iyei ha'Yam quotes the son of the Vilna Ga'on who testifies that the Vilna Ga'on called the Maseches "Beitzah" in contrast to the practice of the Magen Avraham, many continue to pronounce it "Bei'a" today. In defense of this practice, it may be suggested that the source for this pronunciation is the Gemara in Bava Kama (3b) which explains that the word "Mav'eh" (from the root "Ba'a") has two meanings: it connotes either praying or eating. The Gemara in Beitzah (15b) quotes Rebbi Yehoshua who maintains that one must divide the day of Yom Tov into two parts and dedicate half of the day "Lachem" ("for you," for culinary pleasure) and half of the day "la'Hashem" ("for Hash-m," for spiritual pursuits such as prayer and Torah study). Since both of these practices are alluded to in the word "Bei'a" as described by the Gemara in Bava Kama, it is an appropriate name for the Maseches which discusses the laws of Yom Tov. (M. Kornfeld)