בגד, בגידה, בבגדו בה, בא גד

The english translation of בגידה as betrayal and deceit being inaccurate. בגידה rather meaning "considering something external enough to oneself to be considered for change", as in "a change of clothing". [Compare with the סמיכות of שמלה and חליפה]. Why should changing political sides at different times in one's life be any more of a "betrayal" then wearing a different shirt on a different day?  Only because of the expectation that one's ideologies and values should be an integral and existential component of who one is. Hence, the negative sense of treachery/deceit that evolved for the word...

בבגדו בה - פר' משפטים then meaning the choice of the אדון to not carry over and maintain a relationship with the girl who has been working for him, or given to him as a פילגש (??) if I've understood the אדרת אליהו correctly on the pasuk, shows his relating to her as an external בגד of his life and not as in integral, irreplaceable part of it. A part of his life that is interchangeable. בבגדו בה (Granted this reads the בבגדו בה as going on the אדון, the thought may still hold true even if you learn the pasuk is referring to the אב in his having sold her... not sure...)

The כתיב then of  ותאמר לאה, בגד (בא גד); ותקרא את-שמו, גד not having to be necessarily a negative connotation of treachery. It simply means a change i.e. a change in מזל.

[I'm tickled by the בא גד - בגד in the pasuk. 2,3,4 vs 1,2,3,4. 9 vs 10.... could we say it's the א that makes the difference between בגידה and Existential Wholeness/Unity.... don't know.   See further שער מאמרי רשב"י על בראשית על אותיות ד' וג' בבריאת העולם]