speaking as someone who has played for many years in an english ceilidh band which doesn't have any of the words 'ceilidh' 'barn dance' or 'band' in the name, I'd have to say I agree with those above who've already said it probably doesn't matter too much so long as your publicity is nice and clear and your website will appear on searches for any of them.

Ceilidh - you will get some people assuming you are Scottish. Or Irish. And being unable to pronounce or spell the word 'ceilidh'

Barn Dance - you will get some people who assume its an American thing and want to wear cowboy hats, dungarees and check shirts. And straw.

Country Dance - you will get some people wanting line dancing to country music. And/or people associating it with the unbearably twee type of thing that they used to be forced into at primary school.

But any of these possible problems will only affect a small number of potential punters and so long as you are clear enough on your website and on the phone about what you actually do I doubt any major misunderstandings would occur.