Does double strike allow a creature to trigger 'whenever this creature deals damage' twice in one combat?

Double strike (CR 702.4b) causes a creature to deal damage in both the first strike combat damage step and the regular combat damage step. These are two distinct game events where damage is dealt, so any ability that triggers on dealing damage will see each event separately.

Under CR 509.2, creatures with first strike or double strike deal their damage in the first combat damage step. Then a second combat damage step occurs (CR 510.1) in which creatures with double strike — along with those without first or double strike — deal damage again. Each step is its own damage-dealing event.

A triggered ability that reads 'whenever this creature deals combat damage' (or 'deals damage') uses the stack independently each time it triggers. So if the ability triggers in the first strike step and again in the regular damage step, it will go on the stack twice and resolve twice — meaning its effect happens twice.

Example: You attack with a 2/2 creature with double strike and the ability 'Whenever this creature deals damage, draw a card.' It deals 2 damage in the first strike step (trigger #1) and 2 damage in the regular step (trigger #2). Both triggers resolve, and you draw two cards total.

Note: If the defending creature dies during the first strike damage step, it won't be there to receive damage in the regular step, but your creature still deals damage to the player (if it was attacking them) or into an empty zone — so check what the damage target is, as it may affect whether the second trigger fires.