I called both of my grandpas Bup. Apparently, that’s how Baby Me pronounced grandpa. My sisters followed suit. Even now, when talking to my cousins who had the same grandpas, I never know how to talk about grandpa because I CANNOT say grandpa, they will always be Bup and to my cousins they are grandpa. They must think I’m a kook. I usually say, “Bup, umm er grandpa”.
My nephew couldn’t pronounce Paula. It came out Peedin, and Peedin I’ve been for 60+ years.
My niece (who is now 29) is named Chloe. When she was a baby, her mother (my sister) and our parents sometimes intentionally mispronounced her name as CH-low. And, that evolved into “the Piece of Chileef,” a line from the old sitcom Soap, in which Gordon Jump played Chief of Police Tinkler, who was prone to spoonerisms, and once referred to himself as “the piece of chileef.”
Close to 30 years later, we still sometimes call her that.
Interesting. I was imagining another origin…
This is so embarrassing, but when I was a young lad I couldn’t pronounce my Aunt Arlene’s name, so for the first 7 or 8 years of my life (until I just couldn’t bring myself to say it anymore), she was Aunt Weenie.
Had bright orangish red hair. My mother would call be “Sam” as in Yosemite Sam. I was a huge baby, over 10 pounds. My Pop called me Butch.
I’m surprised he let you get away with that. My only maternal cousin is Joseph ____ IV. (and yes, our great-grandfather was still alive when he was born) Great-Grampy was Joe Sr, Grampy was Joe to everyone but his parents who called him Junior all his life, and my uncle was Joey. So naturally, my cousin was “Baby Joey.”
At least until he screamed at us when he was five “I’m not a baby! Stop calling me Baby Joey!” And from that point on he was Joey 4 
My husband had an uncle who was Howard Jr, so they called him Junior. When his son, Howard III was born, be became Junie, and so he remains (he’s close to 70 now.)
The grandboy is named James (and will NEVER be called Jim or Jimmy, etc!!! per mom). His paternal grandfather has the first name James (but uses a different name), and an uncle with the first name James (but uses a different name). The nickname I use for baby James is “Three”.
My son got called Smelly Belly, and my daughter, Stinkerbell - for obvious reasons. We never referred to them as that to other people, of course.
My husband often called the boy Monkeytoes, and I called the girl Pretty Bit or Pretty Girl.
None of these stuck past preschool age, luckily for them.
I called them both Sweetie, of course. Saved me the trouble of remembering their names 
My mother gave a friend’s son a nickname that stuck with him most of his life. He was really such-and-such the Third, but Mom jokingly declared that he should be called Joe. My nephew also goes by a name unrelated to his actual name; bro and SIL jokingly said at an ultrasound, “He looks like xxxx”, and that (not xxxx, just don’t want to cite his name here) has stuck.
My one brother and I both got called diminutives of our middle names, and THOSE have stuck, with the family. Think something like “George Robert Smith” and being called “Bert”, or “Beri”. “Bert” is at least a semi-real name but my brother grew to dislike it and went with George as an adult. I was stuck with the equivalent of “Beri” - as in, not a name anyone has ever used, and not spelled intuitively either. I shed that as soon as I could (the nuns did me a solid there by refusing to call me by the made-up name, and insisting on the Church-sanctioned first name).
My other siblings get called by a fairly standard diminutive of their real names, like “Jim” for “James”.
As a tot, I was called, “Puddin’,” by my mother. And now, back into therapy for me; thanks, FCM!
Me and my brother were both referred to as “Rat Cheese” by my uncle. My cousin was “Chicken Bear”. 
I have two children. I call my son Mr. Man, or Sir. I have no idea why I do that. He is only 1 year old so I don’t know if it will stick. My daughter goes by a nickname and probably will forever because I’m a terrible mom or at least I couldn’t see the future. She has a speech delay with significant articulation difficulties and I also named her Persephone. She has a really hard time with basically all those sounds. We call her Sophie, which is is able to say.
In the same vein, I have a little story about nicknames. I have always called my grandmother Grandma Janice. That is what she has always been to us grandkids. So I was SHOCKED when one day, when I was in college and visiting her, she answered a call from her sister and said “Hello, this is Eileen.” It turns out that Janice is her middle name. I don’t know why we all call her Janice while her siblings call her Eileen. But that’s what it is.
My sister-in-law was the same way with her son (my nephew), when he was born: she made it clear that his name was Nathaniel, and wasn’t going to be shortened to “Nate” or “Nathan” or anything like that. He’s now 21; when he was a little kid, he was sometimes nicknamed “N” by his parents and my wife, but as he got to be a bit older, even that pseudo-nickname went away. He’s always Nathaniel now.
Before my son’s birth I mentioned some names being considered and a friend was surprised that “Scott” was a name being considered. I asked her what was wrong with the name Scott and she said everyone would call him Scooter.
I’ve known many Scotts, and not one of them is nicknamed Scooter.
Yeah, that’s news to me.
While I’m sure that some people do nickname a “Scott” as “Scooter,” I’m not sure that it’s as natural or common of a nickname as @kayaker 's friend thinks.
There’s a Wikipedia page listing well-known people who have been nicknamed “Scooter;” only one of them has the given name Scott.
There is a fairly well-known mathematician whose real first name is Alexandra, but for some unknown (at least to me) is called Gugu by everyone who knows her. Everyone except her second husband (Saul Bellow) who always called her Alexandra.
I had a great-aunt Nancy and a great-uncle Dan, my maternal grandmother’s youngest siblings who survived past toddlerhood, and they were the 7th and 8th out of 10 children. It turns out that they were not actually named Nancy or Dan, but Anne and Richard. Nancy and Dan were not their middle names either.
Turns out that my great-great grandmother decided when they were born that she liked Nancy and Dan better than Anne and Richard and would only call them that. And by the time they were each in school everyone called them that too, including their parents.
Apparently when they were still very young my great-grandmother said in exasperation “Mother, you could have told me you liked those names before they were born and we would have put them on the birth certificates! After six older kids we were out of ideas and just thought Anne and Richard sounded okay!”
I have a second cousin who grew up in Quebec. His English was fine, but he spoke with an accent. He had an Aunt Katherine always called Aunt (or Auntie) Kitty.
At boarding school, he told his teachers that his “Antiquity” was coming to visit. They were prepared for a very much older lady, but she was quite young as she’d married her 40 year old husband when she was 18. We tended to refer to her as Antiquity (when not in her presence). She thought it was a good enough joke to repeat but didn’t like to be called that.