The choice of whether you wish to update your new name in your property title document (eg. Certificate of Title, Subsidiary Strata Certificate of Title and Lease) is yours.
However, if you choose not to update immediately after your change of name, you can do so when a subsequent instrument or instruments [eg. Total Discharge of Mortgage, Mortgage, Transfer (sale)] reflecting your new name is/are lodged against your property title at the Singapore Land Authority (SLA).
Your solicitor acting in that subsequent transaction will at the same time of the lodgement of the subsequent instrument furnish to SLA the necessary documentary evidencing the change of name (eg. certified true copy of your Deed Poll or NRIC reflecting your new name).
Caution Note: The above policy/procedure is subject to change by SLA and/or law, and the reader is advised not to rely on the same or seek proper legal advice.