There is not within the drill down dimension definition.
You would need to create those calculated dimensions in the load editor where you can do aliases.
For example, in the load editor
Project_Name as [Project Name],
Phase_Name as [Phase Name],
if(PMStatus='Open',Company...... as [New Field Name],
Once you make the change, hit 'load', then back in the UI you will have 'Project Name' , 'Phase Name', and 'New Field Name' as nice clean dimensions for your drill down dimension.