Indeed.
For almost all US equities the Depository Trust Company (DTC, subsidiory of DTCC, one of the main US clearing agencies) is the central securities depository (CSD) in the U.S and maintains records of ownership at the institutional level (not individual investors) of brokers/custodians that are participants in the DTC system.
Your (direct counter party) custodian (or their sub-costodian) is merely a record in the CSD database (e.g. IBKR holds x securities of US company XYZ).
Your custodian (your direct counter party) in turn keeps record of who of its customer owns which shares that it itself “holds” aka has-an-entry-for in the CSD database (e.g. IBKR “holds” x security of US company XYZ, and IBKR keeps and updates records of who of its customers A, B, … Z hold how many records of the x shares of XYZ).
If you “register” your securities in your name, all that happens is that your custodian (your direct counter party) notifies – usually for a small fee – the issuer company of your shares in the company so the company can send you its annual letter and whatnot.
If some black or otherwise colored swan were to step on DTC, it wouldn’t matter who your (direct counter party) broker/custodian is. DTC ultimately holds them.
More details on the mechanis here: Underlying stock markets mechanics (advanced level) - #48 by Your_Full_Name