If you are a P.Eng. offering services to the public under a name other than your own, i.e. under a Certificate of Authorization, it is the entity holding the Certificate of Authorization which needs to carry insurance. If you are assured that such a policy exists, you are covered if you practice under that C of A. You do not need to be named either under the C of A or under the insurance policy, because neither are typically specific to the practitioner- licensees and unlicensed people working under a C of A can come and go as long as there remains at least one signatory P.Eng. who takes "professional responsibility" for the work.
If you are practicing as a sole proprietor, it's a different matter. In that case, you and the business are the same entity.
A lawyer may be able to advise you whether or not the limits of liability may be set aside and the corporate veil pierced to come after you and your assets personally in the case of fundamental breach of contract, gross negligence, or for provincial or federal fines etc. You're not going to get reliable advice on that from an internet forum I'm afraid.
Here's what OSPE's website says about their secondary liability insurance offering, which is limited to $125,000 per claim and $1,000,000 total:
What is Secondary Professional Liability insurance?
Secondary Professional Liability insurance protects individuals against liability or allegations of liability for injury or damages that have resulted from a negligent act, error, or omission that has arisen from your activities as a professional engineer. This coverage is intended to supplement existing professional liability insurance, which members may hold through their employers or their own policies.
It is important to note that coverage is afforded on a "claims-made and reported" basis and will respond to claims made during the policy period. This means that the policy which is in place when a claim is made will be the policy to respond – regardless of when the incident occurred. Therefore, it is extremely important there is no lag or gap in coverage between policy periods. Coverage needs to be continuously in place to ensure you are continuously protected.
(end quote)
I would imagine the value of that insurance represents perhaps $20 worth of value in return for OSPE's annual fee, which is what, $180/yr? You'll have to assess whether or not that is good value for money, which I guess is determined by how likely you feel that your work is to get you sued personally.