I'm a skype user, i never create a real account of me the reason is i transaction with some strangers on internet, and i'm very scared to showing my face, i usually make a call if we're talking about the business, yeah the privacy is number one, just never showing your face they (the scammer) can screenshoot it, create a fake id, claim your account (like on exchanger) or doing something bad with it, telegram is another option i think.
That would be the safest thing for us to do since their are so many frauds using skype just to make people believe that they are legit, And their are other as you said that can steal your identity and they will surely use it from different bad schemes around here so better we should be more vigilant upon using skype and use dummy all the times.