Pamela - such things can be confusing but we can't advise you on what you should do in such cases. We register the outcome of such considerations/decisions so if you are unsure as to what's best for the surviving owner and beneficiary then please do seek legal/financial advice.
Your Q is a frequent one so the following may help understand the options although really aimed at what to do once a decision has been made.
We don't use the term 'tenants in common' on the register. Often joint owners will apply for what's known as a form A restriction to be added and that protects the trust, wills, TIC arrangement. The protection is simply that it restricts the sole surviving owner from acting alone when for example selling the property. See our online guidance
Joint property ownership: Overview - GOV.UK (www.gov.uk)
Often joint owners make arrangements to protect what happens should one of them die. For example a trust deed that states that the survivor can continue to live in the property until they too die but their half share of the beneficial ownership goes to X. In such cases a surviving joint owner might simply update the register using form DJP and supporting evidence. The form A restriction protects the beneficiary/trust interest.
In other cases the surviving owner and beneficiary may decide to transfer the legal ownership into their joint names. IF so then the surviving joint owner transfers (TR1) the whole legal ownership to themselves plus X. Things to consider here might be does X own another property or intend to? What impact does becoming a legal owner then have on X and how does that change the trust/wills etc?
And a third option is do nothing. The death is very sadly factual so the register can be updated at any time. If they were TIC and a trust deed/wills exist and everyone is aware of the details then the register stays as it is and everyone is on the 'same page' so to speak.
So the only real advice we can offer as to what to do is to seek legal/financial advice to ensure all parties understand the legal position and the impact of not only the death but also what may or may not happen next re the surviving joint owner and beneficiary - a lot to consider and understandably it can be confusing but that's where the wider advice comes in
Our
online assisted guidance helps link you to the correct guidance and form(s) needed once you have decided what, if anything, needs to be updated/changed on the register
Hope that helps