I have a visual studio add-in project where I must iterate through the current project's items, utilizing the absolute (or relative) path to those files.
The item.Document.FullName works, but only for files that are currently opened.  
Is there any other way to access this information in the DTE object?
Is this what you're looking for?
myProjectItem.Properties.Item("FullPath").Value
                        Even I was looking for a solution to get the project name based on the document or file Name. I found it by using the DTE object.
Initialized the DTE object like the code shown below.
EnvDTE80.DTE2 objDTE = this.GetService(typeof(SDTE)) as EnvDTE80.DTE2;
Then I used following code, to get the name of the project.
var projectItem = objDTE.Solution.FindProjectItem(document);
var projectUniqueName = projectItem.ContainingProject.UniqueName;
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