Your name should have changed if you applied initially. I would suggest you talk to the immigration officer during your interview after the test. He is going to validate all your documents and you can mention about the name change. Local office can accept a name change request during the process of the application. Better to complete this process before the Oath as you ahve all the documents right now.it's not missing any part. my last name is the same, but my first name is now changed to a new name, and I already attached the name change certificate to the application at the beginning. but the citizenship test invite came under the former name.
My main concern is to have my correct new name on my certificate and passport.
https://www.canada.ca/en/immigration-refugees-citizenship/corporate/publications-manuals/operational-bulletins-manuals/canadian-citizenship/admininistration/identity/name-change-requests-purposes.html