According to the Rambam the Kohen Gadol pronounced the 4-letter name, see MT Avodat Yom haKippurim 2:6
Thus he mentions God's explicit name ten times on this day. On all
occasions, he recites the name as it is written, pronouncing His
explicit name (shem hameforash).
The Rambam elsewhere (Hilchot Tefila 14:10) defines the shem hameforash as yue-kei-vav-kei
They recite [God's] name - i.e., the name י-ה-ו-ה , as it is written.
This is what is referred to as the "explicit name" in all sources. In
the country, it is read [using another one of God's names]: אדני, for
only in the Temple is this name [of God] recited as it is written.
This is also how Shulchan Aruch Harav 621:8 has it
Ten times in the course of Yom Kippur the High Priest would utter
the Four-Letter name of G‑d as it is written — three times in his
first confessional: “Please, HaShem, I have sinned…; please, HaShem,
atone…; ‘before HaShem you will be purified’ ”; three times in each
of the second and third confessionals; and once at the lottery
[concerning the goats to be offered], when he said [concerning one of
them], “A sin-offering for HaShem.”
Your rav might have alluded to other views as mentioned there in note 23 "Other authorities understand the term Shem HaMeforash differently in this context (see the Reshimos of the Rebbe, Booklet #41)". One of these views might be the one of R Bachya ben Asher (quoted here).