Well, not exactly...
You will have to register a domain name to have the ability to access your computer like that. If your school offers it though, I've seen things similar to that, but that would be through your school since they would have already registered the:
that you'd be trying to get a subdomain of.
The cheapest place I've found to register in the US:
However that's for a single domain. If you want something like:
Then you can get it for free from:
There are many other services out there that offer this kind of domain name if you are interested. A search will reveal quite a few that are mentioned from time to time on this site.