No. Investors look to the confirmations and statements that they receive from their brokerage firms to confirm their positions as option holders or writers.
An option holder looks to the system created by OCC’s rules, rather than to any particular option writer, for performance of the option he owns. Similarly, option writers must perform their obligations under the OCC system and are not obligated to any particular option holder.
Since every options transaction involves both a holder and a writer, it follows that the aggregate rights of option holders under the system are matched by the aggregate obligations of option writers.