How important to you is it that his name goes on the certificate?
For me it was very important. I wanted him to acknowledge and accept this was his child, even if he chose to then ignored him in every other way. I also wanted my son (and everyone that the certificate would ever be seen by) to know that he had a father and who he is.
The way I got my dc's father to agree was by involving his mother. I pointed out to her how I felt, what I thought it would mean to my ds in the future etc. She was instrumental in getting him to sign up. However this was before automatic PR if father was on certificate, so I may well have thought differently if I was doing it now.
Please be assured the certificate will not say 'Unknown', it will simply be blank.
Also the details can be entered in the future if agreed/ordered by a court, so don't worry that this is something that is permanent and must be solved now.
Also you will still be able to claim maintenance and/or involve the CSA without his name on the certificate. Your ex may well be thinking he can avoid paying maintenace if he isn't on there, but that is NOT how the CSA work.
However, as others have said you should be aware that with his name on the birth certificate he will automatically get PR (parental responsibility) and he will then have responsibilities to his child should he wish to fulfil them. These include access to medical records, choices on school, giving permission to go abroad on holiday to name a few.
Some difficult ex's simply pick and choose which 'responsibilities' to fulfil and it may seem to you that he chooses the ones that make your life most difficult. However any issues like this can be resolved in court should it come to it. For example if you go to court and get residency of your child then you can take them abroad for up to 28 days without needing the permission of others with PR, as long as you inform them.
If your ex wants PR later a court would most likely grant it to him anyway, assuming there is no good reason that he shouldn't have it. If he has shown no interest and suddenly wants PR he would most likely need to show to the court that he was serious about being a parent and it wasn't just whim or purely to make your life difficult.
So the most relevant question on this issue is why is it important to you that he be on there?
Also if he's not responding to you I would suggest, instead of asking him when he can come simply tell him when you are going and that he is welcome to join you. Put it in writing so he can not deny receiving it, and can not say he was unaware of your intentions. Make sure he is unable to say you didn't give him the chance to be there now or in the future (in court or if your ds asks).
And if he is still being stuborn then think about involving his mother and set out your reasons to her and to him why you feel this is important to your child.