Unfortunately. this is a very real problem for many people. Any major "irregularities" in the name of an author—particularly the first author—can cause problems. You don't even need to use non-English characters.
I know this from first-hand experience. I have very little problems with most of my papers—except for those I have published with two colleagues as first authors, one of whom has a hyphenated last name and the other whose name contains an apostrophe (compound Dutch name). On a regular basis, I need to write places like Web of Science to correct the publication records (e.g., the paper is listed as a cited reference, but somehow they can't seem to connect it to the original record, depriving us unfairly of citations). This has actually been a bigger problem with the hyphenated last name—the paper has about six or seven citations (provable!), but only one is listed in Web of Science. (Google Scholar seems to find them all, though.)
Other problems will also crop up in attendance lists, email accounts, registration for conferences, and other things where Unicode acceptance in databases is limited.
Note, however, that your professional name does not need to match up with your legal name. For instance, many female academics keep their maiden name if they started publishing under it when they were graduate students. This is the case even if they've legally changed their name after getting married. And I agree with Armand that it is more important that you use a consistent name—once you decide which version you want to use, stick with it!