Michael becomes マイケル (Maikeru), and John becomes ジョン (Jon). When foreign names are written in Japanese, they are usually written in katakana to match the sound of the original name as closely as Japanese allows. The meaning of the name is not translated into Japanese.
Foreign sounds cannot always be copied exactly. Japanese simply does not have every sound found in English and other languages.
For example, Smith is usually written スミス (Sumisu), and Chris becomes クリス (Kurisu). Extra vowel sounds are added because that is how Japanese pronunciation works. Long vowel sounds are often shown with the mark ー. Paul, for example, is written ポール (Pōru).
There is not always only one possible katakana spelling. The same name may be written differently depending on the language it comes from or how the person actually pronounces it. If you already use a Japanese spelling of your name, that is usually the safest version to keep using.
The order of the family name and given name is a separate issue from katakana. Western names are often written in given-name-first order, as in ジョン・スミス (John Smith). Names from cultures that normally place the family name first, such as many Chinese and Korean names, may keep that order. Writing a foreign name in katakana does not automatically mean rearranging it into Japanese name order.
What about using kanji instead?
You could give John characters such as 城音 simply because they resemble the sound. But to a Japanese reader, this would usually look more like a playful kanji name or nickname than the normal Japanese spelling of John. The ordinary way to write the name is still ジョン.
People whose names are originally written with Chinese characters are different. Many names from China and Taiwan, for example, already have their own characters. Keeping those characters is not the same as inventing kanji for a Western name afterward.
Writing a foreign name in katakana does not give the person a new Japanese name. It simply puts the original name into a form that can be read and written naturally in Japanese.
