Inconsitency on birth certificate

[baraider]

On my parent's birth certificate, the city of birth of that time was called differently than it's called today.
Which one should I use throughout the paper? How it's called today or how it's called on their birth certificate?

 

[BornintheRSA]

I would put "New Name (formerly Old Name)" just to be safe.

 

[baraider]

THANKS.
Another query: The place of birth on my mom's birth certificate and passport are different. Which one should I go by?
My guess would be to go with the birth certificate but just want to confirm.