Numbers appear with country code in message app A friend of mine just bought an iPhone. She imported all her SIM contacts using the regular method: Settings &gt; Contacts &gt; Import from SIM All went well.  

But when she opens the Messages app, the list is filled with numbers with a country code prefix, so instead of the normal overview of conversations (Tom Dice, David Swimmer, Kim Bauer, etc.), she gets a list with all the numbers of her contacts as name (+324123456, +328945782, etc.).

So, has she imported her contacts the wrong way? Or Iis there some corrupt data in her phone? Or what?

I know it's a pretty vague question without a screenshot, but if you need any more information, please let me know.
It might be how the previous phone she had save the data on the sim card and the iPhone couldn't import it properly and misplaces the data in the import processes.

I suggest you try once again with the same phone with different sim card [or even the same sim card and see]

This will make sure that the phone doesn't have a problem.

Because to me the importing data from sim card most likely a software issues which easy to solve.