In The Hobbit: An Unexpected Journey, we see the contract for employment of Bilbo Baggins as a Burglar with the company of Thorin Oakenshield.
At the end of the contract, the area designated for signatures looks like the following:
So where Bilbo signs the contract, it is clearly mentioned that he was signing as The Burglar. Not only this, he's referred to as Burglar in the entirety of the contract .
Yet, in The Hobbit: Battle of the Five Armies, when Bilbo is asked to show any official document with his name or signatures on it to prove his identity, we see this:
[Auctioneer:] “This is most irregular. Excuse me, it’s been more than thirteen months since the disappearance. If you are, in fact, Bilbo Baggins and undeceased - can you prove it?”
[Auctioneer:] “Oh, well, something official with your name on it would suffice.”
[Bilbo is, justifiably, quite flustered.]
[Bilbo:] “Alright! Right.”
[He pulls out the contract that he’d signed to join Thorin’s company and looks through it.]
[Bilbo:] “A contract...of employment as a...a...nevermind as what.”
[He shows it to the auctioneer.]
[Bilbo:] “There! My signature!”
[Auctioneer:] “Uh, certainly seems to be in order. Yes, seems there can be no doubt.”
So if it was evident by the signature and the contract that Bilbo was working as a Burglar, why would he bother trying to hide it? If he was ashamed of being seen as a professional burglar, how does not saying it out loud help when the truth is mentioned everywhere on the contract? He points out his signature, so assuming that the contract required signature only at the end of the contract, it should have been obvious to the auctioneer that he was employed as a burglar, given that the caption next to the signature says "Burglar".
As pointed out by Bellerophon, he may have been trying to avoid saying it in front of everyone present at the Auction. But why would he expect the Auctioneer not to gossip about it? In a small community like Hobbiton, I'd expect such a thing to be fairly common, gossiping that is especially when the gossiping material is so uncommon. "Oi, did you hear about young mister Baggins? 'E went off working as a Burglar, he did. Saw it with me own eyes."
Is this how the event transpired in the books as well, assuming it happened in the books at all?
NOTE: While I have watched the Peter Jackson movies an embarrassingly high number of times, I haven't read the books.