The question is not whether it must have a meaning in chinese: I agree with you that anything written in Kanji automatically has a meaning. This applies not only to Chinese, but also to Japanese, where, one needs, for some sense of need, a Kanji name for his/her official stamp. The question is whether one is allowed to `invent' a name. So, if there never has been a MeiLi in known chinese memory, can one still name a baby MeiLi?
My question about iceland is which of the following statements best (in the sense of mutual information across all nations or national identities) explains the law that one needs an icelandic name (Incidentally, I am guessing icelandic name does not mean `has a meaning in icelandic', rather it means `has been historically used in iceland'): (a) iceland is worried about its culture getting diluted. (b) iceland is European (c) iceland is Judaeo-christian-muslim
Note that a country might easily explain its own rule by quoting (a), but it is possible that the best explanation is not actually (a). For (a) to be the best explanation in my sense, one has to check whether a disproportionately high fraction of nations with similar rules also are worried about the culture or vice-versa; compared to similar statements with (b) and (c).