No need to purchase dedicated domain..until you like to access WCF service with it. or Just IP will do.
Have a look in steps given here:
http://stackoverflow.com/questions/1712778/how-do-i-host-a-wcf-service-on-the-internet[
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1. I am assuming that you have made a working WCF application and hosted over the IIS.
2. The next thing to do is to browse the application from the IIS. It will give you url in the address bar something like: http://localhost/myservice/service.svc
3. Next go to www.whatismyip.com. this will give you your system's WAN IP (say, 45.34.56.200).
4. Replace the URL you got in step 2 with: http://45.34.56.200/myservice/service.svc
5. Now you can use this URL any where in this world to consume your service.
Hope this will help. Thanks.