How to modify to a different phone number after having activated the plan?

Go to your account
My Plan
Manage
Change this phone number

Chizz :))

My question is how to change the phone number linked to the actual phone plan

Sorry I don't think understand your question.
The only phone number you get to link to your account is the one active with Fizz.
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Earlier answer was to show you how to change your Fizz number.

Chizz :))

You can't port a new number after it's activated. You can only do as Rene said, change to a new number from fizz pool.