If you are the PA (i.e., person been sponsored), I don't think you have to wait......what's most important is that you provide the proof of change of last name after your marriage......include the proof of change of last name in your application package.
The most important ID, is your travel passport.....because your last name in the forms has to be as shown in your travel passport......Refer IMM0008 Personal Details Full Name.
Its not mandatory that your include a copy of your passport when you submit your application.....but has to make sure you send a copy of your passport to IRCC later and before PR visa issuance........so if you are changing your last name......fill the forms with your new last name......then apply for a new travel passport with your new last name, and then send a copy of your new passport to IRCC later.
Refer.....checklist......
Note:
Although you do not need to have a valid passport or travel document when you submit your application, you must have a valid travel
document or passport to be able to travel to Canada and to be admitted for permanent residence.
https://www.canada.ca/content/dam/ircc/migration/ircc/english/pdf/kits/forms/imm5533e.pdf
If you are the Sponsor, I don't think you have to wait........what's most important is that you provide the proof of change of last name after your marriage......include the proof of change of last name in your application package.
