What kind of drop down are you refering to? Something on a template? A custom property that inherits from a base class?

The built in drop down-list property where the values (name/value) are set through custom property settings. I want to translate the name for editors depending on their personal language when in edit mode.

When I look at the source code it seems that we try to find a translation for each value if it starts with a '/'-character. So basically you should give values like "/mytranslationpath/value/" and make sure that you add the correct translations to your language files and it should work.