Why is the Gemara concerned about figuring out who the Tanna of a Mishna or Braisa is?
Thank you for your question.
There can be a number of reasons why the gemora feels it is important to know who the tanna of a certain Braisa is. Firstly, because it has to fit with other statements that thus tanna has made. More important, if we can figure out who the Tanna etc. is, by bringing a proof of it, from a different source it will then give us a deeper understanding as to the reason why Tanna is saying this. For example there are numerous times when the gemora will say that this Mishna is like the following Tanna, because the Tanna in the other Mesechet said a similar halacha, and the two have the same logic. The gemora will then refute the proof and show that the two cases are not the same, and therefore the logic of this Tanna is slightly different. By using such a process, we gain a lot of understanding why the Tanna said what he did. There may be many other reasons, but for now this should suffice.