Did Stilgar have a Sietch name? Was the fact he was a Naib mean he didn't need or use one?
I don't recall other character being referred to with their Sietch name other than Muad'dib (Usul).
According to the Dune Encyclopedia, it might have been Sahkan
(10141-10228). Most generally described as Stilgar the Fremen or Stilgar the Naib, but in his youth as a wali in Umbu Sietch, known by his birth-name of Tuan. It was not until 10153, when he became a sandrider and accompanied a group of other youths on a raid against a Harkonnen village that he acquired the name by which he would be best known. (His troop name, used only by his comrades at Umbu Sietch, is thought to have been Sahkan — the Fremen name for a type of desert hawk — but verification of this point is difficult to obtain. The evidence found thus far consists of a reference made by a man from that sietch who accompanied Stilgar on jihad.)
For the record, another character whose sietch name is explicitly confirmed (in the Extended universe novels written by Herbert's son) is Liet Kynes.
More than a thousand desert men uttered his sietch name over and over. “Liet! Liet!”
That being said, no good explanation is provided why this name would be used outside of the sietch by other Fremen in Dune, nor why they would use it in front of outsiders. Put that down to bad writing.