How can the idea of reincarnation be true if all the information of who we are is already destroyed Because our consciousness can only persist in our brain. When the brain is destroyed, our consciousness is destroyed as well. We become no one. 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.
if you take it literally, Buddhism does not teach "reincarnation" because to actually reincarnate, there has to be something permanent like a soul to transmigrate from one life to another.  Consciousness is not permanent.  It raises and falls all the time.    Now, to understand "reforming" in Buddhism, you need to understand "Satanam/being".  it is  another term as difficult as nirvana because it does not have sign or dimension or anything/.. Buddha said "because ignorance as barrier, desires as bindings, satanam continues to moves in samsara".  In my own words, there is a thing outside of time and dimension that latches on consciousness and takes it as self, me, mine..  as long as ignorant and desires persist, satanam will latch on another consciousness when this one connected to your brain ceases to work.   As long as that feeling we all have that we call "I, me, my" exist, when this body is broken, the "I, me, my" will instantly latch into other body and call that body (5skandhas) as ours.  Do not take satanam or "being" to be the same as permanent soul.   here is link to look up being or satanam