Who is my son’s next of kin

You are. Unless he's married when he dies then his wife/husband is. Try to get him to write a,will, it's not hard and can be done cheaply. It will save you a lot of hassle if something happens to him unexpectedly.

You can name anyone as next of kin, it doesn't need to be family. I was next of kin to a dear friend of mine who was many years older than I, I didn't know until she was rushed to hospital.

Just to be clear, you can name anyone as 'next of kin'. It has no real legal status, and is mostly used in hospitals and similar situations. So your son would probably name you in those circumstances
If someone dies without a will, then the estate is distributed as the link above explains - and whoever your son wished to be called his 'next of kin' has no bearing.
Your son can make a simple will for free (donation to charity requested) at certain times - usually well advertised by local solicitors.
He can also make a simple will, cheaply, by using LawPack forms: www.lawpack.co.uk/
They are not suitable for anything other than the most straightforward of wills, but better than nothing! DH & I have used them at a couple of points in our lives when money was tight and the instructions were simple.

Being next of kin confers no legal status.

The fall back position is the nearest blood relative, but you can nominate who you like.

When I was looking after my uncle who suffered from severe depression. The rather unpleasant psychiatrist(that is another story) who was meant to be treating him insisted that his brother was his next of kin and that my uncle did not have capacity to make his own decision, even though he wanted me to fill that role. So I asked his brother to write a letter saying he was too unwell to fill the role (which was true, he was in a care home) and delegated the role to me.

Next of kin has no legal standing whoever they are.

My aunt who was very close to her brother my Dad and visited each other at least weekly was rushed into hospital Nit expected to live, when my dad visited his sister he wasn’t allowed to see her at first as he was not down as NOK ,her carer was !!! he had to get his sisters permission, thank god she wasn’t unconscious to change it so that he could even visit her.

It appears my aunt was totally under the carers helpful ‘spell’ and had been taken by her to get her pension each week etc When she died ALL her money had been wiped out she was actually penniless without even her next months rent. it came to light that the carer had had a new family car and lots of expensive family holidays
My aunt died soon after we found out her flat had been emptied of anything of value We tried to prosecute the carer but she said my aunt thought of her as a daughter and had willingly given her ‘ presents. We could prove absolutely nothing It broke my Dad

Talk to your son and advise him to get a will made, especially since he has people he wants to make bequests to. I can never understand people who don't make a will, it leaves one helluva mess behind that takes months to sort out. I speak from experience. I have made sure I have my will and POA in place.

Anyone can be next of kin if someone decides that is who they want. Because most people tend to choose close family members, it does not follow that it has to be and where someone has to be appointed it is done on th basis of closest relative.

I was next of kin for an uncle by marriage. His brother was older and iller, so he said I was his next of kin.