Be honest...If it was Conway when you were there it doesnt matter who it is now. If you put down CFI and never actually worked for them when it was called CFI....you just lied on your application. It doesnt matter who it was, or the name of the company or even if they still exist. You give the information to the best of your knowledge and let the recruiter do their job and find out about you. Offering too much information is sometimes a red flag. Makes us look like we are hiding something. Just tell the truth and nothing more.