Which one would you say is the correct spelling?
Mohamad, Mohamed, Mohammad, Mohammed, Muhamad,
Muhamed, Muhamet, Muhammed, Muhammet, Mahammad
Transliteration is the term used to describe the process of representing words or letters of one system of writing in a second, different system (e.g. Arabic to English). The name محمد is a good example. The issue here is that, in Arabic, vowels are rarely written. They are often understood from context. Hence, the name Mohammad is actually represented with its four consonants and written as: MHMD (محمد). This practice leads to different ways of pronouncing the same word in different dialects. So, when the word is transliterated into English, it is represented with different vowels depending on which dialect or language it was originally taken from. Persians (Afghans, Iranians and Tajiks) usually spell it as Mohammad while Arabs pronounce the first vowel more deeply and thus spell the word as Muhammad. Turks (and people in the Balkans) pronounce the final d as a t which leads to spellings such as Muhamet or Muhammet.
When using transliterated words, a good strategy is to go on a search engine, type your best guess and then limit the search to your target geographic area. If you see only a few hits, your spelling is perhaps not the most common one.
If you simply want to find the accepted spelling of a word, just type each spelling in the search box and see which one yields the most number of results. Mao Zedong gives 1,940,000 hits on Google whereas Mao Tse-tung gives you only 827,000.