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Is there a way to Callout label the anatomy parts of the (i) knee, (ii) lungs, (iii) eyes in one body chart? For purposes of this question, the labels can be "knee", "lungs", and "eyes" respectively.

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One possible way: add the labels as you would in Graphics3D using the properties "Name" and "RegionCentroid" as label and position of Text primitives:

AnatomyPlot3D[{Entity["AnatomicalStructure", "LeftHand"], 
 Blue, FontSize -> 16,
 Text[#["Name"], #["RegionCentroid"], {-1,0}]&/@
 {Entity["AnatomicalStructure", "DistalPhalanxOfLeftThumb"],
  Entity["AnatomicalStructure", "DistalPhalanxOfLeftIndexFinger"]}}]

enter image description here

Alternatively, construct a separate Graphics3D object for labels and use Show to combine it with AnatomyPlot3D:

 Show[AnatomyPlot3D[{Entity["AnatomicalStructure", "LeftHand"]}], 
 Graphics3D[{ Blue, FontSize -> 16,
   Text[#["Name"], #["RegionCentroid"], {-1, 0}] & /@ 
  {Entity["AnatomicalStructure", "DistalPhalanxOfLeftThumb"],
   Entity["AnatomicalStructure", "DistalPhalanxOfLeftIndexFinger"]}}]]

same picture

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