The throne name (praenomen) has the following four hieroglyphs, listed by Gardiner number as:
𓎟 V30 (basket)
𓏥 Z2 (three strokes)
𓆣 L1 (dung beetle)
𓇳 N5 (sun)
I think the issue you are having is with Z2, the plural strokes for the plural. However, Z2 is classified as a determinative, indicating plurality. Because it was often paired with hieroglyph G43 (quail chick), which does have a phonetic value -w, the Z2 is often transcribed as
(w) within brackets.
Although it looks like Z2 (three strokes) is "before" L1 (dung beetle), as a determinative it simply adds to what is physically above it, not what comes before it in phonetic order. Hence the plural determinative Z2 is "attached" to L1, and so we should parse it as:
L1 (dung beetle) - Z2 (three strokes)
Hence we have
nb-ḫpr(w)-rꜥ. Adding conventional changes, we get
Neb-kheperu-re, which becomes "Nebkheperure" in modern standard Egyptological writing.
There is also the fact that many (most?) of the other pharaohs of the 18th Dynasty had a throne name ending in the same thing. So we have Aakheperure (Amenhotep II) all the way down to Djeserkheperure (Horemheb).