In a second season scene in Star Trek: The Next Generation, Dr. Pulaski mispronounces Data's name with a soft vowel in the first syllable.
There's actually some backstory in the exact pronunciation of Data's name. Slash Film explains that no one had determined how to pronounce Data before the first table-reading of a scene with Brent Spiner (Data) and Patrick Stewart (Jean-Luc Picard). Gene Roddenberry has present at this event.
Stewart pronounced Data with a hard vowel, which came as a surprise to Spiner. Roddenberry immediately accepted it as a canonical decision. Furthermore, he established that on Star Trek: The Next Generation, whichever actor says a name first determines its pronunciation.
-via reddit