Japanese symbols mainly consist of three forms; Kanji, Hiragana, and Katakana. Firstly, children at school start learning how to read and write Hiragana and Katakana characters which of these two forms are considered to be part of the basic knowledge of the Japanese writing system, and relatively easy to memorize in terms of not only their shapes but also the limited numbers of each character with compared to those of Kanji characteres. In Japan, people's names can be written in all of these Japanese symbols. In everyday life, people in Japan need to write their names in either or all of these Japanese symbols depeding on what is required for a particular situation. It is also noted that names of people from foreign countries are usually written in Katakana symbols but some of them prefer to use their names translated in Japanese Kanji symbols.
You can actually use all of these Japanese symbols (Kanji, Hiragana, and Katakana) for your name. As we mentioned above, since names of people from foreign countries are usually written in Katakana symbols, it would be always a good idea to have your name translated in Katakana symbols. If you are asked to write your name in Japanese by native Japanese speakers, then it is expected that you write it in Katakana. On the other hand, if you are getting your western name in Japanese symbols for tattoo designs, artwork, or having fun, it's completely ok to have it translated in Kanji symbols. In fact, even Japanese people enjoy converting their names or names of things in different Kanji symbols for fun.
For more information about the Japanese symbols, please check out Japanese Symbols - Design For you.