Assuming you are using mapped objects in your tests .....
You need to set up your object in such a way that a high level change (such as a base part of a URL) changing is easy to manage. So set your mapped objects up with the base part of the URL (usually it will only be a base part of a URL that changes - in different environments etc) is paramaterised as Project Variable.
So when the URL changes, you simply update the Project Variable with the correct URL and all your objects will still be recognised. (My current web project does this)
If you are going to use name maps for objects, you need to give some thought to how you'll use them to identify objects and how to make them maintainable. if you just use the recorded objects, without any checking and tidying up, you are likely to run into problems like you're having at some point down the line. There is no one answer that works in every scenario, different projects and setups will need different ways to set up their name maps depending what they are and how they are likely to change over time. Name maps can work, but only with careful setup and planning - if you want to avoid problems.
More info on using parameters to identify mapped objects here:
http://support.smartbear.com/viewarticle/57310/(which is nested within the link nishnatha already gave you)
