Given the revolutionary tenor of the Dead Sea Scrolls, my guess would be that the Teacher of Righteousness is a nom de guerre.
Noms de guerre were adopted for security reasons by members of World War II French resistance and Polish resistance. Such pseudonyms are often adopted by military special-forces soldiers, such as members of the SAS and similar units of resistance fighters, terrorists, and guerrillas.
This practice hides their identities and may protect their families from reprisals; it may also be a form of dissociation from domestic life. Some well-known men who adopted noms de guerre include Carlos, for Ilich Ramírez Sánchez; Willy Brandt, Chancellor of West Germany; and Subcomandante Marcos, spokesman of the Zapatista Army of National Liberation (EZLN).
During Lehi's underground fight against the British in Mandatory Palestine, the organization's commander Yitzchak Shamir (later Prime Minister of Israel) adopted the nom de guerre "Michael", in honour of Ireland's Michael Collins.
https://en.wikipedia.org/wiki/Pseudonym#Noms_de_guerre
My guess for the identity of the Teacher of Righteousness is Saddok, the co-founder of Fourth Philosophic Judaism (c. 6 CE), based on my view of the DSS as being largely Fourth Philosophic writings in doctrine and timing (given that the majority of the DSS are dated to the Herodian era) and because the Teacher and Saddok were "righteous ones" (or zaddiks). We don't know much about Saddok other than his name and Pharisaic background and the fact that he co-founded Fourth Philosophic Judaism, but that role is certainly similar to the Teacher, who founded the sect that produced some of the DSS (which arguably evince intimate awareness of Pharisaic Judaism).
Another option for the identity of the Teacher of Righteousness I've considered before is James the Just (of whom it is said by Epiphanius in Pan. 78.14.2, "
He was no longer addressed by name; his name was The Just"), and while their respective doctrines and biographies seem similar to me, James' timeline is an issue due to carbon dating of the Habakkuk Pesher up to 2 CE (plus or minus however many years). Saddok's time seems less problematic in that respect (all the more so if he was teaching within mainstream Pharisaic Judaism before breaking away in 6 CE, as per his Pharisaic background).
But I think the similarities in doctrine that I see between the Teacher (whether he was Saddok or not) and James could be due to Christianity being a version of Fourth Philosophic Judaism (i.e., Jesus' version). Jesus and the Teacher and Saddok and James were Fourth Philosophic zaddiks, in my view, whoever the Teacher may have been. That's why Christianity is so similar to but not exactly the same in every particular as some of the DSS, I think. They're both products of Fourth Philosophic factions, with Christianity being the most successful.