Who to notify of citizenship:
Registration to be an elector is separate for Municipal/Local elections, Provincial elections, and Federal elections; so when an election is approaching, the new citizen who wants to vote needs to register to vote for the Municipal/Local election, and similarly for the Provincial election, even if they checked the application box to have their name registered with Elections Canada (that only registers the new citizen for the Federal election).
At the time the new citizen renews health care coverage, it is also a good idea to specifically inform the respective health care insurer (such as OHIP for residents of Ontario) that you are a citizen. (I did not notice until much later that the renewal form specifically listed my status, and even though I became a citizen before renewing it lists me as a "Permanent Resident.")
Depending on which bank you do business with, you may want to update the bank's information about you to reflect your status as a citizen. Updating this kind of information probably has little if any significance, but some may want their bank to have the correct, current information. (Status has only come up, for me, in relation to making RSP contributions; might be something a client seeking a mortgage or business loan should have current.)
Beyond that, I stooped to much bragging to family and friends, letting just about anyone who knew me know that I am now a Canadian citizen. Nearly two years later, I continue to regularly wear the maple leaf pin I was given at the oath ceremony. To my mind, anyway, becoming a Canadian citizen is indeed something one would like to let the world know. Brings me a smile every time I think of it, despite all the cause for sadness and sorrow in the world.