@sunshine11 - but OP's DH, the father of her child, IS Irish. Little Cillian is half-Irish and half-English/Scottish/Welsh or whatever the OP is.
By the same logic OP can't give any DC an English/whatever she is name either as her DH would also be giving the DC that name, and he's Irish.
This is the downside of being half and half. I get it myself 'oh you can't use a Welsh name as you're not properly Welsh', from the same people who object if I support England as I'm 'not properly English' either.
I guess any DC I have shall remain nameless as I'm too English to use a Welsh name and too Welsh to use an English one 
Also, Cillian is not a silly name. Names from other cultures aren't silly. I would advise anyone to think of potential pitfalls of a name - for example I would avoid Myfanwy in England as to someone who doesn't know how to pronounce it, it looks like Myfanny - but that doesn't mean other Welsh names (or Irish/Scottish or any other cultures names) are verboten.
There are plenty of people with Celtic names in England - Tadgh, Aoife, Seán, Orla, Eoin, Caoimhe, Saoirse, Ailbhe, Mari, Seren, Siôn, Ioan, Aneurin, Eira, Eirlys, Tomos, Alys, Tesni, Taliesin, Morwenna, Jago, Elowen, Lowenna - none of these names are stupid, and neither is Cillian.
Remembering that Cillian is Killian, not Sillian, is not difficult when said Cillian is your grandchild/newphew/cousin. OP's family are perfectly capable of pronouncing it correctly, the issue is that they are choosing not to!