This one's complicated but interesting. A few days back, it was revealed by the developer of an app called Doodle Monster that Doodle Jump creators Lima Sky (we've talked to founder Igor Pusenjak before) was trying to enforce trademark rights against any app on the store using the word "Doodle" in its name. That creator originally planned to step down and change the name, but the creator of another app called Doodle Hockey instead spoke out to say that Lima Sky had no business claiming the word "Doodle" itself, that there were pre-existing properties and trademarks on the word, and that "everyone with an app containing the word 'doodle' in the title needs to stand up to Lima Sky's threats."
Now, Pusenjak himself has spoken out on the issue, and he says that he's retracting the original notice from the App Store. But he does hold his position on the word "Doodle," saying that "there was absolutely no rush to call a game 'Doodle Something' until Doodle Jump became famous. Then many developers began jumping on the bandwagon whether their game had any doodled elements in it or not. They were simply trading on the fame of Doodle Jump, for which Lima Sky has a trademark." Pusenjak admits that there is a trademark in the system before Lima Sky's, but says that the company's complaint on the App Store was designed to protect Doodle Jump against anyone else's attack.
At any rate, legal action aside (and it doesn't appear as if there will be any), Pusenjak has agreed to step back from the restrictions, which even he agrees went too far, and says that he's simply trying to avoid customer confusion -- any developers creating games that might be confused with pre-existing IPs should simply have to change them, not remove games entirely. That seems to make sense, so hopefully that agreement will stand without further clashes.