Sounds like your stepmother has a lying problem. A dear friend of mine is a chronic liar. I used to get upset, however, her lies are minor- and nobody is ever harmed by what she says. Her lies always make her stories seem a little more dramatic, etc. I can even tell now when she goes from truth to lie, but it has taken years. I honestly do not think she can help it. Because I value our friendship, I let it go.
As far as nicknames go, I would let it go. I have experienced both sides of the nickname game. My brothers name is Christopher. We always called him Christopher, not Chris. Whenever anyone called him 'Chris', my mom would correct them. His wife now calls him, 'Chris'. Ugh. But its not his nickname that truly bothers me- its his wife. I have issues with her on other areas. He himself isn't bothered when someone calls him Chris.
His son's name is Robert. My mom called the baby, 'Bobbie'-and instantly his wife had my brother correct her. No way were we to call him anything but Robert. Being on the corrrected side, I can say that the nickname thing shouldn't really matter if it is not insulting in any way. My brother has always always called me, "Sissy". So, I called myself "Aunt Sissy" to the baby. Oh no- his wife won't allow that. I am Aunt Kim. Terms of endearment is what a nickname is.
My husbands family is full of nicknames, in fact, if you ask someone what his and his brothers real names are-they have to really think hard to get them right.
My kids also have nicknames. My stepdaughter has been called 'Bug' since she was born. Even her coaches call her Bug. My youngest kids have been given versions of their own names ie; Kay for Kayla, Ry for Ryan, Tiff for Tiffany...also Tiffy, Princess,Punkin etc. heh heh heh...my youngest answers to Tater, Kayla Potata, Katie, Kaylala, etc.
Our oldest is pregnant with her first child. I truly do not like the name she has chosen. At all. It isn't an easy name to make a nickname out of either. But when one comes up, I hope I will be allowed to use it- or else he will be called something like Pumpkin.