Strangers, on first acquaintance, frequently call me by a nickname form of my first name. I never use the nickname form, so they’re not following my lead, but most people quickly or eventually end up using it – usually quickly.
I’d imagine this happens all the time for Thomases or Fredericks too.
Some names, though, people seem to tend not to abbreviate right away, or without hearing someone else who knows you call you by the nickname version. Maybe because they are not obvious contractions (Jack for John), or because there are multiple possible nicknames for a given name (Rob, Bob, Bobby).