I was told at first it was possible, then when I tried to change my account from my name to my company they told me no. I tried 3 times and all said it is not possible.
Now keep in mind that all Uber related expenses from car payments, repairs, car insurance, gas and anything else incurred for Uber are deductible from your Uber income. You need to have your start and end odometer reading, the percentage used for Uber is the deduction percentage.
Because Uber uses the simple method for GST/QST in Quebec, you just need to worry about the total amount paid as you won't be able to claim the GST/QST back like you would in a regular business.
If you are able to do it, they may have changed the rules, please let us know in this post.