Would a PC who lost his brain than had regenerate successfully cast on him have his memories, or we he forget everything. Would he slowly regain memories or just never “remember” how he is or was?

I'll be quite surprised if the "general" answer to that question will not be: "that is ultimately up to you as a DM to decide!" 

Generally, losing your brain would mean you die and you cannot cast Regenerate on an object (a corpse in this case).  But as stated above, it is ultimately up to you and what you think makes sense.

Intellect Devourers magically devour the brain when they take over the body, but once they leave, the body is still alive and if you can restore the brain within 1 round they stay alive, and if you don't they die. Their statblock states it requires a Wish spell.

Also, point of note: Regenerate spell only works on the body 'members' such as limbs. It has no effect on internal organs. 

For all other forms of regeneration it depends on the specific feature. A troll can regrow its head, for instance. In fact, sometimes it gains additional ones. There is nothing stating they get amnesia so one could say they regain memories too.

Various forms of fiction can have memory recorded not only in the brain but also in the soul or the eidos of that person. Certain traits, powers or magic can restore memories from that soul or the eidos when restoring a brain. There is no set concept for or against this in D&D 5th Edition that I can determine, but as it tends more to the magic and souls and less about physical biology it's can be easily assumed it's more "soul" than "brain". There are features that can involve swapping bodies described as transferring the soul, with no mention of transferring memory yet there is the heavy implication of it since knowledge and training are indeed transferred.

So , very likely, a restored brain includes restored memory, and the general idea of...

Quote from Vince_Snetterton>>

 No brain = instant death.

.. is demonstrably false in D&D 5th Edition given the multitude of exceptions.

From a pure human biological standpoint I would say no.  A regenerated brain would not have memories.  Memories are encoded not just by connections between neurons, but by a specific combination of a network of neurons.  So it's not enough to just put the brain back together, the brain must be put back together such that all necessary neurons have a connection to each other.  But even then, the sequence of neurons firing that correspond to a specific memory would be lost forever and not possible to reprogram so to speak.

However, as Cyb3rm1nd pointed out many forms of fantasy and fiction tie memories to more than just electrochemical signals in your brain.  Since D&D is heavily fantasy themed an argument could be made for that side of things as well.  

If it were my game, I would probably say no, regenerate couldn't restore memories (regenerate can't restore internal organs at all).  But something like a Wish spell or Divine Intervention could. 

I'm wondering now whether a Reborn needs to have a brain.  Like what it it had no internal organs and its body was filled was straw (which was flavor offered at least in the UA).

Quote from MidnightPlat >>

I'm wondering now whether a Reborn needs to have a brain.  Like what it it had no internal organs and its body was filled was straw (which was flavor offered at least in the UA).

 
I don't see why not.

Sentient items have minds, souls, memory, powers and abilities while lacking brains. So it's not like there's no precedent (and another example of how "no brain = death" is false). 

As other said, I don’t think regenerate would work.

Now, true resurrection would work and restore a missing brain. And then I’d say yes, you would get back your memories. 

If you want to make it sort of interesting, and a long road to recovery, perhaps something like restoration may be worked to regenerate the brain.  But then the party will need to devise ways of bringing the literally brain dead character's INT/WIS/CHR back up through a variety of magics.  I could also see some Weekend and Bernies type shenanigans if the body and vacant brain can be somehow magically puppeted (maybe aggressive use of dominate person?).  This is definitely not a ruling, and rather all sorts of liberally abandoning potential rules strictures to figure out ways to make the catastrophe possibly fun or an adventure mini campaign in itself.  As an added complication with a "ghost in the machine" flavor, while the party works to recover this PC's mind, the actual mind has been reconsituted in a technically brainless Reborn.  

I understand the no brain no life but I’m granting a chance for these 1st time players. 

I would say no memories but perhaps a strong enough regeneration would restore the brain. You’d be at an infant level likely to start. For memories and such, a deal with the Raven Queen is in order....