Nearly every share bought through a broker is registered to Cede & Co., the nominee of the depository at dtcc, and your ownership exists as a book entry on your broker's records. This is what makes same-day electronic settlement and lending possible; certificates would make modern volumes impossible.
The trade-off is that you are a beneficial owner rather than a registered holder. Corporate communications reach you through the broker, voting runs through a proxy chain, and in class action or corporate action deadlines the broker is your interface. In a broker failure your claim is a customer claim, backstopped by rule-15c3-3 and sipc.
Investors who want a direct relationship with the issuer can use direct-registration-system instead, accepting slower transfers and no ability to trade until shares are moved back.
Related: direct-registration-system, dtcc, rehypothecation, rule-15c3-3, sipc