Cuahuitl (MH631v)

The combining form for both nouns, tree and eagle, is the same: cuauh-, although, as Gordon Whittaker (2021, 90) points out, the vowel length is different, with cuauh- for tree/wood and cuāuh- for eagle. So, these are near homophones in the stems. In this case, the gloss says Cuahuitl, which would easily be represented by a glyph of a tree or some wood. But perhaps the artist was concerned that the reader might read it as ocotl (torch pine) or some other tree. So, he added the eagle to ensure a phonetic reading that would start cuauh-. If so, then the eagle is a phonetic complement which helps ensure the correct reading. Another example of this glyph has a similar arrangement, but it has added color.

Why a Nahua man would have a name relating to tree or wood may have something to do with the significance of the metaphor, in tetl in cuahuitl (the stone, the wood), which the friars (such as Sahagún, Book 6) described as having an association with knowing secret things.