Lionardo is the Italian version of Leonardo. The first name roughly means "strong as a lion." The choice of the name reflects Leonardo's family's pride in their hometown, as the lion "Marzocco" is the emblem of Florence.
In Italy at that time, it was customary to indicate the father's first name after one's own. Leonardo's father was named Piero, hence the name Lionardo di Ser Piero da Vinci.
Leonardo's family had owned land for many generations in a place called Vinci near Florence. That is why they used the suffix "da Vinci," which means "from Vinci." It was not a noble title, but simply an indication of their place of origin.
The title "Ser" was an honorary title for jurists in Italy, and Leonardo's father Piero was a notary in Florence. Therefore, Leonardo's full name was Lionardo di Ser Piero da Vinci, which means "Lionardo, son of the jurist Piero from Vinci."
Likely upon completing his training, Leonardo referred to himself simply as Leonardo da Vinci. Like other Renaissance artists, such as Michelangelo or Raphael, he is usually referred to by his first name alone, Leonardo.