My question involves name change laws in the State of: California

Hello,
I want to change my maiden name to husbands last name after marriage. I also want to drop my current middle name (fathers name).
But my marriage certificate shows my husbands first name as middle name after marriage. Will there be any issues if I want to drop my middle name now. in ssn office or DMV or passport renewal.

For ex my name is Jane John smith. ( John is my fathers name)
Marriage certificate shows after solemnization- Jane Peter Myer
Husband name - Peter Myer