Is there any central management of public and private key pairs in blockchain? Is there any entity in the blockchain that maintains record and manages public/private key pairs of all the users?
No, there isn't.  Bitcoin has no central management of anything at all.  

Public keys are pseudonymous and in general it may not be possible to identify the user to whom a public key belongs.  A private key is kept by the user who generated it, and typically is never revealed to anybody else.