Is there a standard list of generally agreed upon ways to write non-Chinese names in Chinese? If so, who decides how they should be written?
My experience in China has led me to believe that there is not one set way to write foreign names.
Other than avoiding funny meanings, it seems to not make a difference. I’ve seen my name written by different Chinese people in many different ways.
I showed my “expert card”(work permit) to many Chinese people, which had my name in Chinese, and they all seemed to think the Chinese spelling was pretty good, but not perfect.
Somewhat “standard” Chinese-izations have evolved for some of the more common Western names. For instance, Tom = “TangMu” (can’t write the actual characters here, but there is a specific “Tang” and “Mu” used for it.) Some common surnames also have developed conventional equivalents.
Beyond that, it’s pretty much anything goes. Best thing is to get a native speaker to help you out.
Along with characters that sound like your name, you will automatically get an associated meaning. Make sure to ask for help from someone who likes you (and is not a prankster 
And the meaning is actually more important than the sound. If there is a symbol that doesn’t have quite the sound you’re looking for, but has a good meaning, you should use it.
For example, if your last name is Nenno and you have the choice to use the symbol “Neh” which is phonetically equivalent to the first syllable but means “pig farmer” or “Nee” which has a long e sound instead of the short e sound but it means “King of Earth”, you should go with the King of Earth symbol.
A number of these sinicizations will also have divergent sources that may be puzzling. E.g. the Sinicization of “John” is pronounced “Yue-Han”, as it is derived from the Germanic “Johann”, not the English pronounciation. No reason other than convention, and no, you can’t unilaterally decide to change it to something closer to “John”, because no one will recognize it. In China, anyopne whose name is John is stuck introducing himself as “Johann”.
a quick search didn’t turn anything up, but there used to be a standard transliteration of Western names into Chinese in China up until maybe 10 years ago. I used to run into it because I have a real (actually several) Chinese names, yet officials used to insist on translating my English name according to standards. Officials no longer insist on how one translates a name these days.
Gregory Peck translated into Chinese is a tounge twister.
yeah but then the “nno” negates it. Would rather be “not a pig farmer” than “not the King of the Earth”? 
Chinese dictionaries sold here used to have an appendix listing common ways of transliterating foreign names, especially place names, into Chinese characters. I’ll check at a bookstore later today to see if they still do.