Before 1946, 科 had many more possible readings such as か, しな, しぐさ, とが etc. In 1946, the Japanese Ministry of Education decided to reduce the number of possible readings for kanji in general, and stipulated that か be the only official reading of 科. This means that in official contexts such as newspapers, documents, textbooks, and so on, 科 can only be read as か. However, the aforementioned rule does not apply to proper names (surnames, place names) such as 尾科, which is some dude's name. In fact, 科 is still read as しな in most proper names, even if it is not considered "official". A little long-winded answer I know, but I hope I answered your question.
I see, thanks. Never thought there were hidden readings like this, guess it's something to keep in mind.
Why isn't shina one of the readings for the 科 kanji?
There is a company called 尾科 and I couldn't figure out why their transliteration of the name is Oshina instead of Oka. Shina seems to be a proper kun reading for 科.