Google Analytics account get the “All Web Site Data” standard name instead of the name of your website.
If you happen to monitor several domains this may be confusing, you simply do not know which All Website Data item belongs to which website.
The problem with All Website Data identifier is not the problem inside the Google Analytics itself.
There is still your website name as a the service folder name. The All Website Data is something like a view on your traffic data.
But it is easy to rename the default description to whatever you like.