Thank you all. I think both go with surname!
We were set on Sebastian. But I am wobbling because whenever anyone asks what name we are thinking of and I say it, it seems to sound like 'spast'ian to my ears, which I don't like for obvious reasons?! But maybe I'm just being silly?! He would be Seb most of the time anyway, I'm sure.
Jude is an old favourite of ours (considered for DS1). But friend used it fairly recently for her DS's middle name. This puts DH off because to him it feels 'used', but I'm not sure that matters as friend's little one only has it as a middle!
This naming business is so tricky!