Target archery:
WA rules say something like "shall be marked with the athlete's name or initials on the shaft". Nothing about numbering.
So that covers competitions to WA rules.
AGB rules say about the same thing...
So the question really comes down to "when do these apply?"
Record status competition, obviously. Club practice, obviously not.
Between that, it's harder to say, because it depends on how the organiser of a shoot chooses to apply the rules. Generally speaking it's better for the organizer/judges to have shafts marked, for ease of identification. If they say "according to AGB rules" then you can understand that they want the shafts marked.