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.
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019