What's in a name?

Apparently not much any more.  In the past few years I've noticed an unusual phenomenon concerning people's names and their lack of reponse to how they would like to be addressed.  When, out of courtesy, I ask an Andrew how he'd like to be called (Andrew being the obvious choice but maybe he'd like Andy or Drew), I'm starting to to be met with a shoulder shrug and/or "it doesn't matter."  And it's happening often enough that I'm sensing a pattern.  Since when don't names matter?
While I readily acknowledge we start out in life being named by someone else, at some point in our early development we assume charge of our own names  - Catherine becomes Katy, Michael remains Michael (not Mike or Mick), etc.  If we really dislike the name we were called at birth, we have the option of changing it either legally or by insisting others call us by the name of our choice.  Our names reflect how we perceive ourselves and are part of our identity.  So when I meet someone who indicates by word and/or deed that what they are called doesn't matter, I can't help but feel I've fallen down the rabbit hole.  
Why don't they know what they want to be called?  Are they afraid that by asserting their preference for a specific name they'll be labeled confrontational and difficult to get along with?  Is consensus really that important to them or do they really have so little attachment to their own names that it truly doesn't matter what they are called?
I'll admit -  I'm baffled and uncomfortable when encountering this situation.  I really don't want the responsibility of naming anyone since the last people who did that were their parents and look how much they had to do to get their child where they are today.  So remember when you're applying for a job the first thing you should decide on isn't what pay you want, what time off you prefer or even what type of work you'd really like to do - it's to figure out for yourself how you want to be addressed.  It's the first question you'll be asked in the workplace and the last chance you'll have to firmly establish your autonomy before being asked to give some of it up in return for a wage.