Welcome to the community!
If you wish to keep your current plan and keep your Ontario phone number, you should note that the taxes on your bill are related to your phone number, not where you reside. So you would be paying Ontario taxes, not BC taxes on your services. Since most plans now include Canada-wide calling, keeping your phone number from a different Province would not incur long-distance charges. However, you should also note that for people from BC calling your phone number, their calls would be considered long-distance, even though you might be in BC. They're still calling an Ontario phone number.
If you'd rather pay BC taxes, instead of Ontario taxes, you would need to change your phone number to a BC one. Your current mobile plan is linked to your phone number and may not be available in other Provinces. Even if the plans appear identical, there might be cost differences between the Provinces. If you would like to change your phone number between Provinces, you'll likely also need to change your plan to one available in your new Province.
If you would like to change your phone number and plan, you will likely need to contact customer service so they can access your account to perform the change. I don't think My Account will allow both changes at the same time. Alternatively, you might consider sending @FidoSolutions a PM. Once they verify some information, they'll also be able to access your account.
Hope this helps 😀