Is there any chance to change display name for my contacts? I even changed it using Skype for Android, but after i opened Skype on my laptop i have the old names again.
You have to do this through the People app now. Find your Skype contact and tap/select it. Then bring up the menu bar by swiping up or right clicking. Select Edit and make your changes. You can save by using the same menu bar.
One thing to be careful of is if you have your Skype contact name linked to other accounts. I found you have to unlink your Skype account so it's by itself, make your changes, then you can re-link it if you'd like.
Hope that helps