SQL Server – How to Connect with Dynamic IP Address

You will be using the servername (DNS) or the IP address of the server. But if you have a named instance (as opposed to the default instance), your servername will be followed by \instanceName.

So, in other words unless you changed any SQL Server Express install defaults, you should connect to the server like this:

yourServerName\sqlexpress

SQL Server Express has a default named instance name of SQLEXPRESS. Also, since SQL Server Express is a named instance, you'll need to ensure that your SQL Server Browser service is running.

Another one. If you are trying to connect to SQL Server from a separate machine, you'll need to ensure that the TCP/IP protocol is enabled for SQL Server.

The above two points can be verified and configured in SQL Server Configuration Manager.

I saw an item on Pinal Dave's blog recently that may answer your question. He suggests adding the line 127.0.0.1 localhost to your hosts file

The full article can be found here

I do note, however, the situation he refers to is a machine that is not part of a domain - if your machine is, then this may not solve it