Praise be to Allah.
There is nothing wrong with a person saying to himself, “I shall certainly discipline you, O nafs” if he is disciplining himself in accordance with the teachings of Islam. Even though Allah created the nafs, the main purpose for which Allah has prescribed religion is to discipline the nafs, purify it, and instruct it to do acts of worship and obedience. To Allah belong the creation and the commandment.
Imam al-Aajurri (may Allah have mercy on him) said:
If someone were to say: what evidence is there for disciplining the nafs? The answer is: The Qur’aan, the Sunnah and the words of the Muslim scholars. End quote from Adab an-Nufoos, p. 9
He also said (p. 17):
How bad is the situation of the one who neglects to discipline his nafs and train it on the basis of knowledge; and how good is the situation of the one who pays attention to disciplining his nafs and knows what Allah has enjoined upon him and what He has forbidden to him, and is patient in going against the whims and desires of his nafs, and seeks the help of Allah the Almighty in doing so. End quote.
And he narrated in his book (p. 13) that ar-Rabee‘ ibn Anas said, concerning the verse “Ward off from yourselves and your families a Fire (Hell)” [at-Tahreem 66:6]: Discipline and train yourselves and your families to adhere to the commands of Allah, may He be glorified and exalted.
And he narrated (p. 14) that Sa‘eed ibn Jubayr said: that is: proper etiquette and manners.
Then he (may Allah have mercy on him) said (p. 15): Do you not see, may Allah have mercy on you, that your Lord Most Generous is urging you to discipline yourself and your families. Pay heed to Allah and make yourselves adhere to that. End quote.
Based on that: there is nothing wrong with the phrase mentioned and there is nothing wrong with giving the group the title mentioned, even if this phrase was not narrated in this way from some of the Salaf, so long as it is Islamically acceptable in and of itself and does not include anything that is not appropriate according to Islam.
If you choose a title that is similar in meaning, such as “Self-discipline” or “Training the nafs” and so on, that is also good. Such words were used as book titles by some of the Salaf.
The oath mentioned is not regarded as compelling anyone to join the group; rather he is a member if he accepts the conditions stipulated in the group.
And Allah knows best.