A hypocorism to shortened a name to a first syllable and add a common diminutive suffix (Andrew -> Andy, for example) makes a lot more sense than shortening a name to a completely unrelated name (Richard to Dick, for example). Further, shortening names to those ending in a "y" or "ie" sound seems to be a natural progression and is common to a number of European languages, not just English.

Culture and tradition are arguably not the same, but the culture appears to be not bowing to tradition to the detriment of your own choices.

Your other comments reminded me of a podcast epidode titled "How Much Does Your Name Matter?"

In the podcast, they discuss a paper that relates to a study on the effect of "invented" names on a child.

Both the podcast and paper relate to the U.S. primarily, so please avoid if you are particularly jingoistic.