Name question, please help

I am about to submit my PERM application. The problem is, I went to a local court to have my first name changed to an English one two monts ago, but so far all my IDs and document still have my old name. I guess if I apply LC using new name, there will be a lots of explaination to do. So I am planing to use my old name for this GC application. Anybody can tell me id it is ok? The name change will show on the Immigration record if I don't imform them?

Thank you very much