Using old name on marriage certificate is acceptable?

[Wedding Crasher 0]

Me and my wife got married in Cyprus. On the marriage lisense / Certificate they put my wife's first name and last name as per her passport . My wife who is a US citizen went back to the states and decided to do a name change for both her first name and last name (to my last name). Her court date to get it approved with the judge is next month. 

I dont know yet how we can we change her new name on the marriage certificate. But lets say we keep the old certificate, will it be accepted when we provide it in the I-130 package if we also include proof of name change? She's getting a new passport with her new names. 

Edited February 21, 2017 by Wedding Crasher

[IcezMan_IcezLady 582]

You don't have to change your name on the marriage certificate.

Anyone that I know has her maiden name on marriage certificate before legally changing name.

The marriage certificate is acceptable with the old name.

 *I have my maiden name on my marriage certificate and never changed it and haven't had any problem*

[Wedding Crasher 0]

Yeah but shes changing both , her 1st and last.