Mohammed, Muhammed, Muhammad, Mohammet, Mohamed, Mohammad. You get the idea. I've noticed over several years that there seems to be no international standard for the way Arabic names are translated into English. Is there a reason for this? Are there standards when translating into other languages? How did Arabic to English translation develop such a unorganized style?
I don't have an exact answer but there are lots of reasons why there is so much variation. First, any script that isn't Latin script will be difficult to transliterate. There are sounds in Arabic that lots of Western languages don't use at all, and so different people have different ideas of how to best represent these sounds with Latin script. Also there are tons of dialects of Arabic. The letter ج is pronounced as a "j" in Lebanese but a "g" in Egyptian, for example. Another big reason is that short vowels usually aren't written in Arabic. Per your example, Muhammad is spelled محمد. The four letters used are basically "m-h-m-d". Therefore which vowels to use will be subject to the translators' discretion.
But that's not to say there isn't any set system. The Hans Wehr dictionary which is generally seen as comprehensive, uses a standardized system to transliterate Arabic words (and this system is commonly used in scholarship, at least in my experience). There are other standardized systems as well, just not one that is universal.
There are actually several standards, however, they're mostly used by specialists in the field.
I can't speak for Arabic, but in regards to other languages there are multiple standards. Russian for example has the Library of Congress system which is probably the most widely used (at least by American authors). But there are alternative methods that are accepted as well.
And Georgian also has a multitude of transliterations. This can make things difficult as several Georgian sounds are very similar-sounding to English speakers (my favourite example is ქ, კ, and ყ; all three are "k" sounds, but made at different positions in the mouth. Thus the use of an apostrophe to show aspirated or not, but even these can be left out for simplicity of reading (though this makes transliteration and pronunciation irritating). Thus most works will note in the peace the system they have adopted, as well as any modifications they made. So even if using an established norm, it may be considerably altered and effectively it's own unique version.