Hi plee22,
You can manage your caller identification settings in the Manage features section.
1 Sign in to your account.
2 In the Manage features section, click Caller ID.
3 To turn Caller ID on or off, use the toggle at the left side of the screen.
4 To change your Caller ID number, click Edit next to your number.
To change your caller identification to a previously used Skype Number or mobile number, select the number that you require from the drop-down list displayed and click Save Settings.
If you want to use a new mobile number as your caller identification:
1 Click enter a new number.
2 Select your country from the drop-down list.
3 Enter your mobile number in the text box and click Verify number.
4 You will receive an SMS text message on your phone containing a confirmation code. Enter this code in the field displayed.
5 Click Verify.
6 If you entered the code correctly, you will see a confirmation message, and your Caller ID will be activated in 24 hours.
Source and more information:
https://support.skype.com/en/faq/fa2561/how-do-i-change-my-caller-identification-settings