Even if we know the arbitrary part of the choice of a puzzle name, I think a good definition should take into consideration the etymology of the puzzle name. For example, I would never say about a hexagonal grid that it is a "latin square", it would be contradictory (I don't think latin squares can have geometrical variations).
For sudoku:
from Japanese sūdoku, from sū(ji) ‘number’ + doku(shin) ‘single status’ after sūji wa dokushin ni kagiru, literally ‘the numbers are restricted to single status’
In this respect, I think that it's hard to label puzzles with repetition of symbols/digits as "sudoku".
Fred