I don't see why it would need to be the same jump in both directions.
The only advantage to declaring a jump with the same type of takeoff and the same number of revolutions to be a different jump would be to get around the repeated jump rules.
E.g., if a skater could do a triple toe in the opposite direction, they could still do two regular triple toes, at least one of them in combination, and also a reverse triple toe without having that count as three of the same kind of jump.
Or they could repeat two more difficult jumps (say, quad toe and triple axel for the top men, or triple lutz and triple flip for the ladies) and also do a regular triple toe and a reverse triple toe without that counting as repeating a jump.
But if the reverse jump were rewarded for extra difficulty, then it could be as valuable to repeat that one as to repeat a jump with a more difficult takeoff or more revolutions, so if you can do the same triple in both directions, it would be worthwhile to choose that as one of your repeats.
Even if there were a way to encourage reverse jumping, it's not likely that we'd be seeing reverse triple jumps any time soon.
And senior skaters have no limits on repeating double jumps, except for the limit of three double axels.
You'd also have to make sure the technical panel would notice the reverse jumping to give credit for it. And account for the fact that it's just possible that a skater would learn a jump, most likely single lutz, to rotate the opposite direction in the air from all their other jumps and not actually be able to do it in his/her "normal" direction.
Make it worth the skaters' while to do reverse singles (expecially lutzes and axels) and doubles.
One possible way to handle it:
In any jump combination or jump sequence, if two listed jumps are performed in opposite directions, then the one performed in the skater's nonpreferred direction gets a bonus to the base value. Maybe double the base value for single and most double jumps and add 1.0 per revolution bonus for reverse double axels and higher.
Say the skater did a double axel-double axel sequence with one of the double axels in the opposite direction. That would be worth (3.5 + 2.5 + 3.5) x 0.8 = 7.6.
Better yet, add the reverse rotation bonus after the sequence multiplier: (3.5 + 3.5) x 0.8 = 5.6 + 2.5 = 8.1.
Or how about double flip-reverse double lutz combination? No pesky sequence multiplier to worry about. 1.7 + (1.9 x 2) = 5.5, same value as a triple flip. Might be a good choice of skill to develop for ladies who just don't get enough height and quickness of rotation to master the harder triples.
The exact values of the bonuses would need some adjustment, but even offering any bonus would make it worthwhile for some skaters to develop that skill, if they wouldn't lose more points on GOEs than they gain from the bonus.