To add to the guys work this is why only the first pattern was targeted where (1) is the first in the CircularPatternFeatures collection.
Dim circPattern = part.ComponentDefinition.Features.CircularPatternFeatures(1)
Here it is for all patterns just loop through the CircularPatternFeatures collection
Dim part As PartDocument = ThisDoc.Document
Dim i As Integer = 1
For Each circPattern As CircularPatternFeature In part.ComponentDefinition.Features.CircularPatternFeatures
circPattern.Parent.SurfaceBodies.Item(1).Name = String.Format("Part_{0:0#}", i)
For Each surfBody As SurfaceBody In circPattern.SurfaceBodies
i += 1
surfBody.Name = String.Format("Part_{0:0#}", i)
Next
Next
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Regards
Alan