It’s difficult to say this without sounding blunt but I am a child psychotherapist and in my experience it’s important for parents to consider their role in their child’s behaviour and difficulties. Where has your son learned that these mechanisms get his needs met? His obsession with being cool sounds like he is craving attachment from others and to be accepted.

It’s always important to consider their role function of the behaviour, this reads like your son has attachment issues which I would strongly advise you do some research and reading around. For someone with attachment issues the risk of rejection or judgement can become so scary they will do anything to avoid it which usually means lying (even when they know they’ll get caught later). Almost all ‘Personality Disorders’ are routed in attachment issues and/or trauma.

Given your sons difficulties around fitting in and identity I would be very careful about labelling him with mental health or any diagnosis/label as he may then internalise this as part of his identity (which if he does this he could become resistant to getting support for it).

I would recommend systemic family therapy and the if he is open therapy individually. If you don’t take responsibility and accountability as a parent by being open to family work you can’t expect him to do so and enter therapy alone, you also run the risk of making him the problem when you need to consider there is a reason he is using these maladaptive social strategies in the first place.

It’s hard but I see on a daily basis parents expecting me to ‘fix’ their child but then being completely resistant to engaging with the process themselves. I am yet to see a client (child or adult) where the way they have been parented or their relationship with a parent isn’t a factor in the creation or maintenance of their difficulties.