There are a couple of things you can do, but nothing that will be easy.
What is happening, is that when the user logs onto the Domain, it is treated as a different user. There is no way around this. But your problem is to keep and maintain the current and existing profiles for the users. The two most common ways are these...
1. Have the user log into the workstation with their new domain account. This will create a new profile. Then have the user log off and have the administrator logon. Copy the user's original profile (with all files) into the user's new domain profile. You will likely need to adjust the permissions for this new profile to match users permissions.
2. Copy all of the user's profiles, from all of the workstation to a common network share. Then in each users account, on the Domain Controller, modify where the location of the user's profile will be located. When the user log's in to the domain, their profile will be pulled from the share and they will have all of their icons, documents, etc.
The above have been simplified. There other environmental variables which will affect and modify these. For example, a Windows 98 workstation may not have an individual profile on that computer, unless you specifically set it up. Then you would not likely be able to pull it from a common network share.
Best of luck.