For informal and unofficial use, you may do whatever you like.
Do you mean you would include (カタカナ表記) as part of the name? Or do you mean 水(ミズ)? Or just ミズ?
If you ever come to Japan, you also may do whatever you like in informal and unofficial use. For anything even remotely official, you will find that things will be expected to match your identification.
Foreigners can have a registered "alias" to make daily life easier. Historically, people of Korean/Chinese ancestry in Japan have made use of this so they could use a Japanese sounding name in daily life to avoid discrimination. It used to be possible to change the registered alias as much as you like, but people started doing that in association with criminal activity so now you can register once only and it can't be changed later. For that reason, I suggest that people new to Japan wait until they get past the early days when they're still in the phase where they're going to do what we all do, which is think up some totally ridiculous kanji version of our names, and end up permanently stuck with something that would make them cringe later on.