THIS QUESTION ISN'T "HOW DO YOU SAY ~"
I'd like to know how to write some words in Japanese. I mean writing hiragana or katakana instead of kanji, like "Barn", I know it's "naya" >> 納屋
>> なや / ナヤ
Which is correct? Because I can't find なや　nor　ナヤ on Google は 日本語 で何と言いますか？

質問を翻訳

For the word なや we almost always write it in kanji 納屋.
But I think you can see it written in hiragana in the picture books for children because they would be able to understand only a little kanji characters.
I think we don't have a proper rule for usage of kanji.... Only kind of an "unspoken rule " exists among Japanese people. Then you should remember them one by one....