Where does the word “Sufi” come from?

Al-Hujwiri rahimahullah recorded several explanations for the word “Sufi”: the woollen garment (suf), the “first rank” (saff), the People of the Veranda (Ashab al-Suffa) may Allah be pleased with them of the Prophet's ﷺ mosque, or safa, meaning purity.

The origin of the word “Sufi” was discussed by the great scholar Ali Ibn Uthman al-Hujwiri rahimahullah, known as Data Ganj Bakhsh, in his book Kashf al-Mahjub:

“Some assert that the Sufi is so called because he wears a woollen garment (jama’i suf); others that he is so called because he is in the first rank (saff-i awwal); others say it is because the Sufis claim to belong to the Ashab-al-Suffa may Allah be pleased with them (Companions living in the veranda of Masjid e Nabwi), others, again, declare that the name is derived from Safa (purity).” [Hujwiri, Kashf al-Mahjub]