Trigger warning: This post might be upsetting to some people with BPD or EUPD because it describes causes and patterns of behaviour that some people don't like to think about. No judgement is attached or implied.
He doesn't just need any old therapy or counselling, that's basically useless to him as it will either validate his world view and not help him, or invalidate it and make him hurt himself more. He specifically needs dialectical behavioural therapy (DBT) from a trained practitioner for a course of a minimum of 12 weeks and he needs to attend every session and do the homework.
BPD is one of the most treatable diagnoses, if the person engages with help and can access DBT and works through it fully. Otherwise they will be stuck in the same patterns of self-sabotage over and over. The problem is, he will not see the need to change while he is with you, and when he has completed his DBT, the face you see might not be the face he is showing you now, you might have to learn who he is all over again from scratch.
Literally everything about him might be different, including his likes, dislikes, feelings about things, all of it, because they might have stabilised. That's the fundamental thing about having an unstable sense of self.
People with untreated BPD aren't all the same but their behaviour is very predictable (predictably unpredictable in fact)...
Seeming embarrassed about his diagnosis is a form of manipulation to make himself out to be a helpless sweetheart who you stick with before he shows another side when he feels differently and knows he can depend on you sticking around. A lot of people with BPD have had extremely traumatic childhoods where their trusted adults invalidated their feelings and where they were habitually not believed about anything. They tend to trust their own version of events and own thoughts and feelings even when overwhelming evidence proves they're wrong. Their coping mechanisms are derived from this. A very good description of the struggle is "go away/don't leave".
Here are some of the coping mechanisms you might have noticed (you have to understand, none of these are conscious decisions to act like this, it's not on purpose, they are innate):
Playing helpless/sweet/lovable when they're scared you won't like them.
Initiating sex and focusing excessively on you to be of value to you.
Being excessively generous and kind to people to try and be liked/of value.
Not being able to cope with alternative points of view to their own, especially if they feel invalidated/disbelieved, they are likely to feel personally attacked by different points of view.
Liking everything you like (what a coincidence!) to be likeable.
Impulsive behaviours (for some it's self harm, others, substance abuse or exploiting themselves in the sex trade, or losing it and shouting at people for low provocations then rewriting what happened later to save face).
Pushing you away over a perceived slight then going overboard contacting you repeatedly, potentially with threats to end it all or hurt themselves (but not necessarily), because they've only pushed you away on the assumption they can count on you to not leave, and now they've done it they're scared you might really abandon them.
These are some of the vast range of potentially problematic things they do that he needs to work on before he can be in a relationship. And all of it feels like real feelings to them at the time. They can make excuse after excuse about why they smashed up your house in a fit of pique because they have completely justified it to themselves based on their world view. There's a lot of overlap with other Cluster B personality disorders, such as narcissistic personality disorder.
And they tend to have no idea at all how exhausting it is for other people to be around them, and take people for granted, and minimise what they did after the fact. A close friend with BPD once said it's like having fragments of every other mental illness all slammed together inside her and different ones pop up at different times.
Note, all of this manifests slightly differently in every different person, not all people with BPD do all of these things, and it completely changes when the person is treated properly with DBT. But they often need a strong reason to go and get treated, and it's a disorder where not many sufferers have insight into the problem or the impetus to fix it.
If you were in a long term committed relationship I'd have different advice but you barely know this guy which is why I think you're opening yourself up to a world of high-octane drama and eggshells if you get involved with him right now.
You need to see all of it with your eyes open, but also, if you are going to stay with him, not judge or blame him for it (but also have really, really strong boundaries because he will test all of them to make sure they're really what you say they are, so he knows he can count on you).
You need to be a very sorted person yourself for this to even remotely work because he is looking for an anchor.