I cannot remember hearing a "dee" sound used like that.
Common diminutives for
German names are "-chen" and "-lein". However both border on the ridiculous and are mainly used in jokes or on other special circumstances, much less for forming actual nicknames and such.
So, for example, a
Peter might become a Peterchen or a Peterlein. Sometimes you need slight modifications before it works, like inserting a vowel or generating an umlaut:
Franz -> Franzilein
Franz -> Fränzchen
Hans -> Hansilein
Hans -> Hänschen
Rene www.AboutNames.ch