ESPNcricinfo has been doing this for quite some time now. Below is a recent example from the third ODI between Australia and New Zealand. As you can see, Kane Williamson was run out, courtesy of a throw from Marnus Labuschagne to Alex Carey behind the stumps who whipped off the bails with Williamson short of his crease.That's interesting, never heard that before, but so few people here in the UK are scorers and umpires with really good knowledge of the rules. I'll have to ask some of the older ex players.
A direct hit run out is generally referred to as an "Unassisted run out" while a run out involving both a fielder and either the keeper/bowler or another fielder behind a set of stumps is called an "Assisted run out". I would doubt this data is kept at international or domestic level but MyCricket which is used in Australia to record games of cricket here includes this function and this data is displayed on scorecards here within the system. Some clubs will award points to such dismissals for Best and Fairest (B&F) or Most Valuable Player (MVP) awards.