stock ledger

or stock book

[ stok lej-er or stok boo k ]
/ ˈstɒk ˌlɛdʒ ər or ˈstɒk ˌbʊk /

noun

a permanent record of the capital stock of a corporation, listing the names and addresses of the stockholders, the number of the shares owned, the serial numbers of their stock certificates, etc.