Writing the sounds of one language, into the text of another language is called transliteration. It happens naturally, when people simply write what they hear, when listening to a native speaker use words or names in the original language. There's also standardized version of it, to ensure the same spelling for the same word. In some languages it's more common to use standardized versions than in others.

When it happens naturally, before a standard version become popular, you can end up with multiple spellings and pronunciations of the same word. For example, besides the most common "Japan", the name of the country has been written as Nifon, Nihon, Nippon, and Jippon.