Although this question should probably have been asked on SE Chemistry, as the molecules are of biochemical importance — and the question is based on a misconception — I will answer it here.
The numbering of the carbon and nitrogen atoms in uridine and pseudouridine is perfectly consistent. The numbering is for the pyrimidine ring, which is the same — uracil — in each case. The different positions of attachment to ribose (N1 or C6)) results in two different structures (and hence names) for the resulting nucleoside, but does not alter the numbering of the components.
[Modified from https://commons.wikimedia.org/wiki/File:Pseudouridine-synthase.jpg‚ Surundu]
Thus N1-methylpseudouridine has the methyl group attached to the N1:
Basis of numbering
The numbering of the atoms of pyrimidine bases derives ultimately from that of the parent, pyrimidine in which the two (indistinguishable) nitrogen atoms are numbered 1 and 3:
The relation of uracil to the parent pyrimidine can be seen from the IUPAC preferred name Pyrimidine-2,4(1H,3H)-dione and a perhaps more easily understood alternative as 2-Oxy-4-oxy pyrimidine i.e. the oxygen substitutions are at positions 2 and 4 (as shown for both uridine and pseudouridine, above).
The preferred IUPAC name for uridine is:
and that for pseudouridine is:
i.e. The formal nomenclature for the two nucleosides only differs in the designation of the position of attachment of the base to the sugar ring (1 or 5 — emboldened above).