Guess it depends whether you want to travel on your own and/or could cope with going on the same trip separate from your ex... assuming you have each paid for your tickets.

If it's a tiny resort somewhere chances are you'll run into each other a lot. Conversely if it's New York it should be fine.

Splitting a PNR is usually easy but you will still be subject to the change rules for the original ticket - e.g. if you've bought one of those 2-for-1 tickets where both passengers must "travel together" there could be a problem. Hopefully this doesn't mean you must be sitting in adjacent seats... so you should be able to find somewhere to sit on the other side of the plane from each other!

I had this "problem" recently on a part-flown nochange/norefund fare - hadn't thought to do anything to the booking - and thought I would be traveling on my own.

When I went to OLCI I noticed I was suddenly the only person on the PNR (Had it been split? Would there be awkwardness on the upper deck at 37,000 feet?) so at airport checkin I explained the situation and asked if they could check that we weren't seated near each other - and fortunately the other party wasn't on the flight at all.