When you send a text message from Skype, the recipient will see the first 11 characters of your Skype Name. For example, if your Skype Name is thisismyskypename, the recipient will see thisismysky. They won’t be able to reply to your text message.
However, you can change the sender ID so it displays your mobile number instead. This means the recipient can reply to your message and the reply will go to your mobile phone (not your Skype).
To change the sender ID, you need to validate your mobile number in Skype.
In Skype for Windows go to Tools > Options > IM & SMS > SMS Settings, click the link Verify your mobile phone number and then follow the steps described.
In Skype for Mac go to Skype > Preferences > Messaging and follow the on-screen information.
After you have validated your mobile number, all the text messages you send from Skype will display your mobile number as the sender ID.
Text messages sent to mobile phones in China, Taiwan and the USA will not display your Skype Name or a validated mobile number. Instead, these text messages will have generic, pre-defined numbers as the sender ID. For texts sent to mobile phones in Russia, the Skype Name is not displayed. A generic number is displayed unless you have set your mobile number as the sender ID.