I'm looking for a word that describes the shortening of a names full spelling that can by itself be a statement or sentence, thanks for any assistance.
My name. The shortened sentence
Example: Ruben A Rodriguez = Rub A Rod
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I believe there is no word for such a specific exercise.
Although, in general, what you are engaging in is wordplay:
playful use of words : verbal wit
There is no word I could find for "finding one word inside another."