Sure it's valid.. and in the US, if I'm not mistaken, it's expressly legal to call yourself whatever you want - as long as you aren't doing so to commit a crime.
So during day to day business and life, you can call yourself whatever you want. Others can insist on identification if it's important to them, and that gets trickier.. but using a pen-name on a book or a hotel reservation is no different than using a fake name at starbucks while waiting for your coffee.
Forging documents is of course illegal, so that puts a crimp on things - but there is no particular reason that you are required to use your "real" name except when dealing with government documents (and things that rely on them)
So during day to day business and life, you can call yourself whatever you want. Others can insist on identification if it's important to them, and that gets trickier.. but using a pen-name on a book or a hotel reservation is no different than using a fake name at starbucks while waiting for your coffee.
Forging documents is of course illegal, so that puts a crimp on things - but there is no particular reason that you are required to use your "real" name except when dealing with government documents (and things that rely on them)