In fact, the daughter of President Trump's first name is "Ivana," just like her mother.
"Ivanka" is a nickname for Ivana, similar to how a child named Robert would be called Bobby or Daniel would be called Danny. Or, you could think of it like the television show "Gilmore Girls," in which Lorelai Gilmore names her daughter Lorelai, but calls her Rory.
With Donald Jr. named after his father, it makes sense that Ivanka's mother would also want to pass her name on to the next generation.
In 2010, Ivanka explained her name's backstory on Twitter:
My actual name is Ivana. In Czech, Ivanka is the baby name for Ivana, like Bobby is to Robert. RT @Saluxious Ivanka, how'd you get u r name?
- Ivanka Trump (@IvankaTrump) December 28, 2010