I can't even put into WORDS how much it irks me. I used to have an aunt (passed away a few years ago,) who ALWAYS spelt my name wrong on Christmas and birthday cards. My name's Helen, she spelt it Hellen... ALWAYS...
Sometimes she even called me by the wrong name. My mom is called Barbara, and she called me 'Barb' so many times!
Also my nana used to call me Shelagh - her sister's name! (Her sister is mom's aunt!)
In addition, a woman I know who lives in my neighbourhood (who have been avoiding for a while as she does my head in,) was bugging me, asking me to do her favours, and being nosey and annoying, and generally pissing me off.
When I said 'no' to 2 favours, as it 'doesn't work for me,' she suddenly, mysteriously started calling me by the name of a 'new friend' she kept going on about (a temp she had met at work.) The woman was a different race to me, half my age, and had a TOTALLY different name. So hers was Consuella and mine is Helen. Impossible to get us mixed up.
THEN, during another conversation, she started to 'forget' my husband's name, then one time, she even claimed that she forgot I had a daughter. 
I had known her 5 years at this point!
IME, and IMO, most of the time, if people forget your name, it's because they don't care about you enough to remember it, or they are trying to make you THINK they don't care (and trying to make you feel bad!) or they are just rude and obnoxious. (Sometimes a mixture of all 3!)
As @littlecaf stated, when you do it back to them, they get very annoyed. I think 'why? You do it to me!'
I know some people genuinely cannot help it (if they have memory issues/early set of altzeimers etc,) but some do it on purpose, or simply don't care about you enough.
An elderly neighbour of ours always puts 'To Pat and Fred' on on our Christmas card. DH is called Pat, and I am called Helen, so I am not sure who Fred is!! And when she sees me she says 'hello Pat!'
But there is no malice there, and she doesn't do it on purpose, she is very scatty, and at least she sends us a card!!!
I do have a few more examples, but this post would be twice the bloomin' length.
disclaimer all names have been changed.....