בר אדא משוחאה

Bar Ada Mishuchah, which means one who measures lands, [and so explains the Aruch and in the margin of the Hilkhot Parashat Masei, it explains the place there]. Rabbi Yehuda said to Bar Ada Mishuchah, "Be careful with the measure," [as seen in Bava Metzia (K’z 2), it is evident, according to the explanation of the Aruch. And in Eruvin, chapter 5 (N’v 2)] Rabbi Abba Bar Ada Mishuchah, "Explain to me [regarding the measurement of boundaries, as Rashi explains there, indicating the boundaries of the city, Bar Ada is mentioned there].

I do not understand what is meant by 'Bar Ada is mentioned there,' it implies that his name is Bar Ada, for if his intention is 'Ada is mentioned there,' it is simple that there are many named Ada. And if his intention is that Bar Ada is his name, from where do we know this? Perhaps 'Bar' means son of Ada."