After the amendment of the name in the holder's NRIC, the onus of whether or not to have the change similarly updated in the Singapore Passport lies with the holder.
To be consistent with the name in your IC, you should change the name in your Passport. You can do so at ICA after you have changed your name in your IC. We strongly advise you to update the name in your Passport before you book your travel ticket or travel overseas. However, if in doubt, please contact ICA directly.
Please note that this query relates to government policies, and we can only provide guidance and shall not be deemed as advice whatsoever.