Chose name for first publication (special characters and compound names)

+1 for thinking about this before your first publication. Have you read through the other questions tagged personal-name? They may be helpful.

In your case, I’d go with Alan võn Neumann, or võn Neumann, Alan if your target journal uses this format.

If you include Chúrch, then I’ll guarantee that you will start being referenced as “Chúrch (2015)” - maybe not on this publication, but later. (You do plan on using a consistent name throughout your sciencific career, right?) Bibliographic databases may be smart enough to pick this up, but they will need to rely on journal editors including your correct name in their journal databases, and this is where noise will creep in.

Conversely, I wouldn’t worry too much about the diacritical characters, as long as their mapping to basic characters is straightforward. Search engines understand this, so it won’t make a difference whether your name is listed as võn Neumann or von Neumann. One exception would be German ß, where it is not obvious that this should be transcribed ss. IIRC, people have legally changed their names over this.

Another option is to write your pen name with a dash: võn Neumann-Chúrch. This could be a reasonable compromise: On the one hand, you can keep both of your actual surnames. On the other hand, the risk of being misquoted is slightly greater than if you drop the second surname (but it is smaller than if you keep both and write them without a dash).

Despite Stephan's comments on diacritical characters, I would still worry somehow about them. I do not know what the state of the art is today, but I saw in horror once an article of mine being from Mylasterrorame instead of Mylastname, with n being a diacritical character.

And yes, Google still finds the wrong version.

I do not care about that anymore (having left the academics world) but, should I have known, I would have dropped anything which is not ASCII in my name immediately.