My parents enrolled me into a medishield plan since young, but they are the policy owner. Is it generally advisable to get my own policy in my name and discontinue this one?

To begin with, it will be good to find out the exact plan that you are referring to. As a Singaporean or a Permanent Resident, you are automatically covered by MediShield Life upon birth. In detail, this policy should be under your name and you can check the details from CPF website.

Read More: Is MediShield Life enough in Singapore

Next, if your parents have gotten a private enhancement, i.e. integrated shield plan, then we will need to find out more about the plan and what it covers. Generally, I will suggest my clients to do a change of ownership to take over the policy as both the policy owner and the life insured. In effect, the onus will be on you to pay for the policy and continue the coverage to that end.

Meanwhile, if the current scope of coverage is insufficient, you may always choose to upgrade the plan to enjoy better coverage. This goes in the same way for downgrading the plan. For this purpose, your parents' insurance agent should be able to offer professional advice and assistance.

Finally, you may read more about integrated shield plan and understand more about how it works: Integrated Shield Plan Singapore: A Starter's Guide

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As far as I know, you can transfer ownership of policies. Just contact the agent that manages this policy and they should know what to do to get the admin done.