Change of new during naturalization

[RR_San]

Hello,

I knew that First/Last name can be changed during applying for US Citizenship, but my question is

1. What will happen to the existing Bank accounts and Immovable properties that are in other country which were in the old name 

2. Can i keep it as it is in the Old name or i have to change it to new name. If i have to change to new name what is the process to do it.

Thank you!  

Appreciate your response.