Two somewhat similar points:
- When it comes to choosing a correct spelling, I disagree with Alexandre Eremenko that one should follow the spelling in the cited paper. I think one should always use the spelling under which the person is best known.
Let's say you are citing several papers by Erdős, some with a non-standard spelling (MathSciNet also lists Erdös, Erdós, Erdőš, etc.) Are you going to have several different spelling of the same author? Only in the references or in the main body of the paper as well? This only creates a confusion and serves no clear purpose (MSN merges all spellings anyway).
Some Russian names gives more unfortunate examples. Are you going to cite Oleinik or Oleĭnik? Gelfand or Gel'fand? The latter spelling is standard in both cases, but few non-Russian speakers would know how to pronounce the names in that case - these extra symbols again create an unnecessary confusion.
- For Chinese and other foreign names - again, the golden rule is to use the name they are best known. I recommend reading this Wikipedia guide which I found to be well thought out and quite helpful.