Probably nobody will be able to give you the exact origin, but shortening names with -(t)z is very common:
- Ulrich: Utz
- Friedrich: Fritz
- Ludwig: Lutz
- Heinrich: Heinz
- Konrad: Kunz
- Dietrich: Dietz
- Gottfried: Götz
- Siegfried, Seifried: Seitz
- Richard: Reitz
Some of these shortened names are not common any more as first names, but are still existing as last names.
Jakob Grimm dedicates a whole chapter of his Deutsche Grammatik (volume 3, chapter III) to the topic "diminuition der Eigennamen" ["diminuition of names"]. But he also just states:
... die ihnen allen zu grund liegende verkleinerung entspringt dadurch, daß der zweite Theil der zusammensetzung wegfällt und unberücksichtigt bleibt, der erste aber durch ein hinzutretendes Z, gewöhnlich auch mit Verlust der zweiten muta, eigenthümlich modificirt wird...
The diminuition stems from the fact that the second part of the composition is omitted, while the first one is modified by an additional z, usually accompanied by the loss of the second plosive.
Grimm does not say anything about the origin of this phenomenon, though. He does, however, provide records back to the ninth century and earlier and stresses the old age of this phenomenon. He also names some records of (rare) shortenings of female names which don't exist anymore, such as Hizila as a form of Hildipurh.
It might also be worth to mention that the same phenomenon can also be found in last names, for instance Schmitz ("smith", instead of Schmied) and Schulz ("village mayor", instead of Schultheiß).