There are many Japanese names because there are different variation on how to pronounce this name. For example, other items such as weapons or people have different Japanese names because they're used for different purposes or different concepts.
For meowth, the name origin "Meow" could mean different things in Japanese based on how it's used. What you should know, is that Moewth's most common Japanese name is: Nyasu (as used on this website.
Hope I helped! :)