I know "Terry" is used as a given name, and derives from french Thierry. It could also be used as a nickname for e.g. Terence. Here the first syllable of the given name is used as the stem in the nickname. Another way to form such diminutive nicknames is to use the last syllable of the given name for the nickname, as in "Betty" for Elizabeth. Analogue to this, I wonder if Terry is sometimes used for Peter or Walter?
Terry as diminutive for Walter is not completely unknown. For instance, in this 2017 book, a character scolds another for saying “Terry” instead of “young Walter”.