We still don't know the significance of Clara's name or the phrase, run you clever boy and remember, but there are plenty of precedents for clues hidden in names and sayings. Epic spoilers ahoy for all modern-era Who.
Torchwood - The defunct spinoff's name was an anagram of Doctor Who. So what's an anagram of Vastra, Jenny and Strax?
Pond - In the latest Xmas episode The Snowmen, Vastra tasks Clara to come up with one word to explain why the Doctor should help her. I still haven't got the bottoms of my Santa suit clean.
River Song/Melody Pond – This is the big one. The climactic reveal of River Song's identity hinged on playing around with her name, specifically a mistranslation of it. Clara's name doesn't easily lend itself to such manipulation, however.
Saxon – Throughout season three, Vote Saxon posters appeared for an upcoming UK election. Turns out, it was evil timelord the Master masquerading as Harold Saxon the whole time! The swine! Don't blame me, I voted for Morbius.
Are you my mommy? - In the Moffat-penned Poison Sky/Empty Child stories of season one, a creepy little ghost kid asks this over and over. And in pretty much every episode since, a creepy little ghost kid repeats some phrase or other.
Bad Wolf – Rose, while TARDIS-possessed, leaves the words bad wolf throughout time and space as a message to lead herself to this final reckoning.
Oops try this instead:
Hello Sweetie - River Song's catchphrase. When these words appear she can't be far behind.
Smilers – A stretch to be counted as wordplay, more like a bad pun, but a very underrated creature from season 5, The Beast Below.
Silence will fall when the question is asked - The Silence did a bunch of stuff and then everybody forgot what it was. And who they were. And that they existed. Because that's what they did. Make people forget stuff. Was that arc ever satisfactorily resolved? I forget, but we know what the question is...
Doctor who? - The Doctor's true name has been teased, hinted at and given great significance for decades. River Song is evidently the only one who knows what it is, but the question remains outstanding. Maybe his real name is...Oswald.
CLASSIC WHO BONUS: Dalek/Kaled - Wordsmith Davros switched the first and last letters of his ethnic group's name to come up with a moniker for his creation. Then he taught them pretty much only only one word. Starts with E. Ends with ATE. HOLY CRAP IS THAT DAVROS' HEAD IN A JAR? HOW THE HELL DID THAT HAPPEN? I NEVER EVEN SAW THAT ONE!
So what other obscure and arcane wordplay has Doctor Who offered up? Was there something in Blink besides don't blink?
EDIT: I don't know how the pics got all ballsed up and not below the text like they were supposed to be and they refuse to be edited! Kinja already balked on this the 1st time I did it.