Hunter's Mark can be applied to more than one creature at a time but only with something like the Sorcerer's Twinned Spell Metamagic class feature.
Otherwise, Hunter's Mark requires concentration and you can't concentrate on more than one spell at a time (PHB pg.203) so you wouldn't normally be able to have it applied to a second creature.
As a strict reading of the Ochre Jelly's Split description and as Miniman points out, it splits into two new and separate Jellies so any effects on the original fade into the æther and aren't applied to either of the two new ones.
What you can do instead
As the DM you have the freedom to bend/break the rules as you see fit to make the game more entertaining and I'd say in a situation like this it'd be a fair call to do so.
Assuming the PC can maintain concentration, allowing Hunter's Mark to still be applied to only one Jelly when it splits isn't really going to break anything since you can change quarries when you drop your current one to 0HP anyway. You could even add a Constitution saving throw to maintain concentration when the split occurs to simulate the change in the creature having an adverse effect on the spell. Doing so brings this ruling closer to RAW and gives the player a chance at not wasting resources because of strict adherence of the rules.
This may also help the player feel less cheated if they only recently cast Hunter's Mark before the split and if the Jelly has high enough HP left after the split to make it's continuation seem useful.