Passport will be enough to prove to almost anyone that you are a citizen with the new name.
You can apply for an updated citizenship certificate but it will take some time and probably no-one will ever, ever ask to see it.
Small note: there are some documents that you cannot change i.e. they are historical like birth certificate (at least in Canada although doesn't apply to you), COPR, etc. I think applies to most things like eg educational degrees or certificates. You'd just show your change of name legal docs to anyone who wants to be sure that you-are-you. Keep a copy handy and probably a copy of those legal docs on your phone.
Then there are documents you can change but don't necessarily have to rush to do - or could leave forever really. Again, you'd show your change of name docs as well as original. The citizenship certificate is an example - change it if you want but basically doesn't matter.
Some things you should change when you renew i.e. not urgent. But probably inconvenient if you don't change them.
Some things you really need to change - i.e. it will just be really inconvenient otherwise.
I think driver's license is considered something uyo have to change. Don't know what else is considered essential.
