Did Pilate really have a friend named Biggus Dickus? Or did Monty Python get it wrong?
Uhhh…no.
As for the movie itself, Python absolutely got it right. 
Not so fast.
This article claims otherwise. The authors assert that Dickus, in addition to his friendship with Pilate, was famed throughout Rome for his speeches outside the Senate House known as Biggus Dickus Ejaculationus.
The above source has proved invaluable to me many times during the course of my research into Roman history, even though it is totally content-free.
Please do not come into GQ and pour cold water on an OP without providing a spurious cite, like I always do.
Duly noted. 
Just to be factual, for a second, giving characters ludicrous names, often describing their personalities, was perfectly within the bounds of Roman Drama. So in Plautus you have Miles Gloriosus – “The Bragging Soldier”, who got an entire play named after him. (Later, Larry Gelbart used the name for one of the characters in A Funny Thing Happened on the Way to the Forum. He also took the name Pseudolus – “Liar” – from another play to use as his main character, played in the movie by Zero Mostel)
I’m not familar with anyone with as risque a name as a latin equivalent of “Large Penis”, but in Plautus’ *Menaechmi[/i there is a Pseudolus-like roguish main character named Peniculus, which means, literally “Sponge”. The name is appropriate because a sponge was used to wipe down the table after meals, getting all the crumbs – and Peniculus is basically a professional full-time dinner guest, a parasite. As one of the commentators on the play has gleefully pointed out, though, the Romans also used sponges as toilet paper.
He’s not the Messiah - he’s a very naughty boy!
That’s nothing, in the Greek tragedy Testicles In Ye Sacke of Rome, our hero Testicles, aided by his pack of Trusty Trojans, penetrates deep into the bowels of mystery to solve the disappearance of the Vestal Virgins.
It’s enough to make a Venetian blind!
That’s pronounced ‘Tes-ti-clees,’ right?
And Cicero means ‘pea’, which is a nickname that stuck with some ancestor of the Cicero we know as a result of the warts in that ancestor’s face.
Biggus Dickus is most certainly a fake name.
Incontinentia Buttocks, however, is absolutely genuine.
That name will either get you a lot of dates or a lot of insults.
No discussion on this topic can be complete without a link to the Wikipedia “Latin profanity” site.
I always heawd it as “Incontinentia Buckets,” as in uwinawy incontinence. I suppose the weading of this line depends on whethew we imagine Biggus Dickus as the sowt of man who pwefews pwodding his lady the nowmal way ow buggewing hew…?
I’m sure he would swell up…
…with pride, you are correct sir!
What about Wudolf the Wed-nosed Weindeer?
Very minor nitpick: “chickpea.” “Pea” was the family name of another of Rome’s great families, Piso, one of whom was Cicero’s sworn enemy. 
:: raises a patrician eyebrow ::
Awe you… wagging me?
I find this whole convewsation wisible.
The best part of this, is that I really am Brian.
No, I’m Brian, and so is my wife!