How can the idea of reincarnation be true if all the information of who we are is already destroyed

Consciousness does not reside in brain. Otherwise re-incarnation of any form is not possible. Consciousness is the holding structure without which body and mind does not function and therefore cease to exist. This holding structure too contains part of memory and therefore memories live for sometime. But even this structure is not a permanent and disjoint phenomenon. It is like a wave which arises and perishes in ocean. You can call ocean of consciousness as super-consciousness from where individual consciousness arise as a wave and then dissolves. But the wave does not dissolve completely. Some part of wave is preserved and some part is picked up from ocean. Therefore suffering belongs to all of mankind not individual. Also mankind needs to evolve to lower suffering of individual. That is the reason Buddha or any enlightened person never talks about it. It is pretty much a complex subject. I have tried to give a very simplified version.

I think the main problem is that you've already claimed to have understood consciousness. I think that you should reconsider your claims about consciousness before attempting to tie it in with the concept of rebirth.

As far as I'm aware, the process of becoming a realized individual in Buddhism involves understanding the nature of something such as consciousness.

Overall, my point is that the information you're seeking is something that only a fairly realized individual can convey to you. If you're really intent on finding out about that, I'd suggest finding a good teacher and learning from that individual.

The Pali Buddhist scriptures contain a number of statements about consciousness that may help decide if consciousness is related to reincarnation, including the following:

• It cognizes, it cognizes': Thus, friend, it is said to be 'consciousness.' And what does it cognize? It cognizes 'pleasant.' It cognizes 'painful.' It cognizes 'neither painful nor pleasant.' 'It cognizes, it cognizes': Thus it is said to be 'consciousness.' MN 43

• And what is consciousness? These six are classes of consciousness: eye-consciousness, ear-consciousness, nose-consciousness, tongue-consciousness, body-consciousness, intellect-consciousness. This is called consciousness. SN 12.2

• Dependent on eye & forms, eye-consciousness arises...Dependent on ear & sounds, ear-consciousness arises...Dependent on nose & aromas, nose-consciousness arises...Dependent on tongue & flavors, tongue-consciousness arises...Dependent on body & tactile sensations, body-consciousness arises...Dependent on intellect & ideas, intellect-consciousness arises. MN 18

• It's good, monks, that you understand the Dhamma taught by me in this way, for in many ways I have said of dependently co-arisen consciousness, 'Apart from a requisite condition, there is no coming-into-play of consciousness. Consciousness, monks, is classified simply by the requisite condition in dependence on which it arises. Consciousness that arises in dependence on the eye & forms is classified simply as eye-consciousness...etc' MN 38

• Were someone to say, 'I will describe a coming, a going, a passing away, an arising, a growth, an increase or a proliferation of consciousness apart from form, from feeling, from perception, from fabrications,' that would be impossible. SN 22.53

• Very well then, Kotthita my friend, I will give you an analogy; for there are cases where it is through the use of an analogy that intelligent people can understand the meaning of what is being said. It is as if two sheaves of reeds were to stand leaning against one another. In the same way, from mentality-&-materiality as a requisite condition comes consciousness, from consciousness as a requisite condition comes mentality-&-materiality. SN 12.67

• It would be better for the uninstructed run-of-the-mill person to hold to the body composed of the four great elements, rather than the mind, as the self. Why is that? Because this body composed of the four great elements is seen standing for a year, two years, three, four, five, ten, twenty, thirty, forty, fifty, a hundred years or more. But what's called 'mind,' 'intellect,' or 'consciousness' by day and by night arises as one thing and ceases as another. SN 12.61

• "Now what do you think of this, O monks? Is consciousness permanent or impermanent?" "Impermanent, O Lord." SN 22.59

Because our consciousness can only persist in our brain. When the brain is destroyed, our consciousness is destroyed as well.

Not necessarily but the brain helps as a more convenient store, hence brain damage can hinder memory. Also why you cannot remember of past lives is that you now have a new brain.

Jhana meditators can recall past lives hence this is not necessarily true as sense impressions have persisted. 5 Hindrances is one case of we cannot remember and as meditation overcomes this you can remember better. [(Nīvarana) Sangarava Sutta]

As for conciseness it arises and passes. At death it passes in one body and arise in another. This process don't end at death or with brain damage or death.

How can the idea of reincarnation be true if all the information of who we are is already destroyed. We are just new when we are born and we can't pass the consciousness or memory to any new born baby.

Sense impressions are tied to the mental body while conceptual impressions are tied to the physical body. So if you get brain damaged you cannot think and perhaps learn new concepts but past impressions stay, [Mahā,nidāna Sutta] these sense impressions do persist beyond death as part of the Bhavanga Citta. Recallability depends on the level of hindrances. [(Nīvarana) Sangarava Sutta] The mental impressions that remain are part of the mind (Nama) which does not die at death but passes away in one body and arise in another. For further understanding perhaps you can study the Buddhist rebirth process.