I recently received dual citizenship (born Canadian and acquired Italian). I am currently in Canada and last entered the country on my Canadian passport. If I decide to leave Canada on my Italian passport, will the Canadian government be aware of this? Are these two passports linked in any way? ie. Is the Canadian government even aware that I am now a dual citizen, since I only dealt with the Italian consulate?
No, there's no such sharing.
Canada doesn't do border control on exit; however the check-in staff will transmit data to the CBSA.
At check-in when leaving Canada, you should always present the Canadian passport, as that is what needs to be recorded by the CBSA.
If the check-in staff asks for a return/onward ticket from the Schengen Area, then additionally present your Italian passport.
As a Canadian citizen, the Canadian government does not keep track of, or care, when or how long you are in the country. You may leave at any time without telling anybody. This also means that you can enter Canada at any time and be admitted (assuming you can prove your Canadian citizenship).
For your specific question, you don't have to travel "on" just one passport. See the answers to the question "I have two passports/nationalities. How do I use them when I travel?", which describes when you need to show each passport at each checkin/border crossing. For a Canadian and Italian passport combination, it's not very complicated because both countries are fine with their citizens having multiple nationalities.
So, if you are flying to somewhere in Europe for example, check in at the airport, show the ticket agent your Italian passport (so they know you have the right to enter Europe and won't be refused entry), and enjoy your flight.
Note that when leaving Europe, you would want to show your Italian passport to the exit passport check. Canada doesn't have exit passport checks.