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I don't think there is a dedicated interface for doing this in the OmniGraffle 5 beta, but there is a workaround (but it probably isn't quite what you are hoping for as it would probably be fairly laborious to implement):

In the Canvas: Selection inspector, there is a new search field which will find any e.g. text you have entered for a shape. How you could set this up to do what you want is to add your object name data as a Note for each shape (or as a Data Key and Data value - also new and in the Notes inspector). Then you can do a text search for that object data and it will select all shapes that share the same Note text (or Data key/value).

In other words, you can use the notes field to add tags to your objects and the selection inspector's search field to select all objects sharing the same tag. For your example, you could enter "Delegate tasks" as a data value for a subset of shapes and search for e.g. Delegate to find them all.

Unfortunately, the only area that this falls down is in copying the Note data to other objects - it isn't possible afaict and you would have to use duplicates of pre-existing shapes instead from e.g. a custom built stencil (either changing their colour and shape parameters manually afterwards or by using the style brush to copy presets to the duplicate shape).