It's the same as Otter Hole being located in Assynt, Fern Cave in Skye and Long Drop Cave in Appin when namesakes can also be found in Forest of Dean, Newby Moss and Leck Fell to mention but three more examples. When a caver finds skulls (even of rabbit) in the entrance of a new cave, a name immediately suggests itself. Hence names do get reused with no intention of causing confusion. Some caves are named for other reasons. No 'Old Ladies' were found, harmed or involved in the exploration of the other entrance to the system, Uamh na Mnathan Uasal an Duror. It was named in recognition of the local teachers who translated the cave names into Gaelic for us - and supplied a patch of ground for our tents.
I was aware of the other Claig-ionn having found it as a result of a search several years ago, but have never visited it. I see that it has an entry in 'Caves of Scotlond'