O H Lee and the Beckley Rooming House

[Jerry Freeman]

And are they claiming that Oswald wrote “O.H.Lee” on this document?

It seems obvious that he didn't. If Oswald was going to use an alias...why not Alek Hidell?
Supposedly, he had an ID in case one was asked for. He failed to have an O. H. Lee ID it seems.

Also, why is it marked “Top Secret”?

For the reason explained above. Any idiot can see that this is not how receipts are kept.
That it was filled out all at once when it appeared certain that Oswald would probably not be back.
That it had been altered for some reason. Also Top Secret makes things sound really important.