I’m in the same situation (married with account at IBKR in my name only).
I named my wife as trusted contact person for the account, so that IBKR already has the name and other contact information.
As I could read in IBKR help, a single-name account cannot be converted to a joint account. The joint account must be created from scratch, and then all positions transferred. I haven’t yet decided to embark on this.
Rights (and splitting) in case of death of the account holder depend on the inheritance laws and on the specific situation (wedding contract, will, …). Normally, the surviving spouse (and children if any) are inheriting, the parents and siblings are not, but this can be modified to some extent in a will.
Another thread of interest is Interactive brokers in case of death