Preserve the certificate as issued. Explain the historic and current place names, using authoritative geographical or civil records where needed and following the applicable document instructions. A country’s renaming does not automatically require a newly issued certificate. Never alter the original entry to match a modern passport.
Building a paper trail across a name change
Say a Boisbriand applicant's birth certificate, an old passport and a current passport each spell the birthplace differently. Rather than filing an incomplete set and promising to supplement it, assemble the civil records first, in the format the official instructions require, with certified translations where they are needed. If a notice from the government restates a spelling you know to be wrong, investigate the conflict and correct the record instead of repeating it.
The official program instructions current on that date, written identification of who receives each payment and under what conditions, a per-person breakdown for the household, and a statement of what happens to any payment if the application is refused or withdrawn. Keep a dated record of the official terms in force when the decision is made, together with the civil, identity, immigration-history, and source-of-payment documents that support later vetting.