Yeah, and I’ve never heard of an attention whore calling himself Mr. Tiny Penis, or Mr. No Penis. Mr. Donkey Penis says two things: Hugely hung and attention whore.
Just to clear some things up…
http://www.johnnydeppfan.com/interviews/playboy2.htm
PLAYBOY: You’re known for dodging attention by using fake names when you check into hotels. But your pseudonyms make good copy. Mr. Donkey Penis?
DEPP: It’s just that if you register as Mr. Poopy, for instance, you get a funny wake-up call. I used to use the name Mr. Stench; it was funny to be in a posh hotel and hear a very proper concierge call out, “Mr. Stench, please!” I never really stayed under the name Donkey Penis. That was an example I mentioned to a reporter once. But I have been Roid, Emma Roid.
A.K.A.?
Urban Dictionary has a bunch of synonyms for “alias” that might remind you of the word you’re thinking of.
Although it’s not the typical usage of the idiom, I’ve heard the term ‘beard’ used in that sense.
Necronomicon? 
The only thing I can think of is sobriquet though it doesn’t quite fit and isn’t very English-sounding .
In his video Tantrums and Tiaras, Elton John named several of his favorite hotel check-in nom de plumes: Sir Humphrey Handbag; Sir Horace Pussy; Binky Poodleclip and so on. My personal favorite, and one Elton says he can’t use in America because of political correctness causing female desk clerks to refuse to use it: Fanny Beaver Snatchclit. Elton commented that he liked the name because he’s always been “a bit of a cunt.” 
The word could be “Bunbury”, of course. But that would be a bit too Wilde.*
For those who don’t get it: See Oscar Wilde’s The Importance of Being Earnest
No, but you just gave me a good idea for this weekend.
I hear there are 14 kinds of guests in a famous pseudonym directory.
Beautiful.
(How long have you been waiting for the right thread to fit this into?)
Cognomen
OK - I’ll bite…
Wha??
There was a famous thread a few years back where someone pretended to ask what the phrase “14 K of G in A F P D” stood for, and while never revealing an answer, kept responding “no, but keep up the good tries, I’ll ask my friend later what it stands for!” Whereas there was no friend, and the phrase was made up to toy with the thread responders.
So this thread sort of reminded me of that, but only in that there are a lot of guesses but apparently none of them accurate so far.
“Signature”?
I am reminded of the Malcolm X movie, where, towards the end, shortly before he is assassinated, and when he knows that his life is very much in danger, he checks into a hotel under the name Mr. X. It occurred to me that he would have been much more sensible, under the circumstances, to have checked in under an assumed name, such as Y.
You can add “[in] mufti” to that list. Usually applied to soldiers’ (often special-ops forces’) and spies’ dressing & grooming like the locals to blend in.
Neil Peart, drummer for Rush, mentions this in his book The Ghost Rider. In the book he takes 18 months off following the death of his wife and daughter (true story) to just travel on his motorcycle an try to survive.
The management firm for the band sets up a credit card account in the name of an alias for Peart with the full knowledge and partnership of the credit card firm. The bills are Peart’s responsibility but the bills are sent and paid by the management firm and deducted from Peart’s share of the earnings of the band. Peart just hands the hotels the card and signs the alias.
Hospitals sometimes do this for even non-famous patients. Some people don’t want information about their condition released except to certain people, so the hospital will work out a fake name so the nursing staff knows it’s OK to give information to someone who knows that name.
I also worked at a rehab that did that as a matter of course. Parents or SOs would get a code name to be able to communicate with their child/SO. The point of this was to make sure that parents/SOs could get through, but no one else. This was to prevent distractions.