Even though labels of Wikidata items were imported from titles of Wikipedia articles and redirects, the label is not updated automatically nor semi-automatically when the original article is renamed. If it is not automatic, it can be a question in the rename dialog (rename the Wikidata label too?).
This could be made optional by providing a check box during page moves. This is quite hard to implement, given that introducing such check boxes is not possible right now (because Special:Movepage is not a FormSpecialPage).
Automatically updating labels seems quite problematic to me. What happens if the existing label does not match the old page name? What about if the existing label still matches a page name for another project in the same language? How do we know when an alias for the old name should be added? How do we avoid adding disambiguation information to labels?
A checkbox would be useful for some people, but people moving pages won't necessarily be familiar with Wikidata's guidelines for labels.
The differences between Wiidata labels and linked pages from other projects should be tracked and listed for review. The lists should be special forms (by language) with clickable service buttons, e.g. "correct the label", "approve the distinction", "suggest for discussion" etc. Handling capitals should be included. Typical cases of acceptable distinctions should be analyzed and described (e.g. synonymic titles, language variations etc.).