Searching for available Apple Developer account names
As far as I know you can pick any name as you like, as long as your company details shared with Apple are correct. And yes, they check everything before you get approved - took me a few weeks to fix the details with them because they've missed the "Inc."

Do you really want to change your future company name if the account is taken as Apple ID? There are many many many companies around with similar names, or near similar names.

Just take the name you had in mind, as long as your company details match there is nothing they can do to disapprove your Apple ID.