Also Irish, also never heard of it as a first name or surname, though it does seem to exist, checking on irishgenealogy.ie.
Instantly my first reaction was that it would be a girl's name to rhyme with Megan.
I imagine that it might be pronounced 'Beegan'
Beagán would make more sense as a name but it is more 'a little' than 'little' so not one I'd personally go for.
I can't warm to it. Sorry OP