I would also suggest マルタ Kate, your name would be written as ケイト

tell me how to write name Kate in Japanese

Thank you very much! Can you also tell me what is the first step to learn japanese. Which system ( "hiragana" , "katakana" or "kanji") I have to learn first?

When I typed your name into google translate, it came up as マルタ (Maruta). I suppose you could use that or マータ (Maata). And the script is called Katakana.

Hi, you can write マルタ. We have "hiragana" , "katakana" and "kanji" and generally we use katakana when we write the person's name, name of the other countries (except some of them) and things which come from other countries. In hiragana, you can write まるた but I'd like to recommend writing your name in katakana マルタ. I hope this helped you.