So what is Sam's full name? Just Sam. Not Samantha. "Sam" is not short for anything, it's not a nickname, that is the complete first name of Tiger Woods' daughter. The middle name, as noted, is Alexis.
So why is Tiger Woods' daughter named "Sam"? Woods explained that when he was a little guy, his father, Earl, used "Sam" as a nickname for him. So we can assume that naming his own daughter Sam was a small nod by Tiger to his father, who passed away about a year before Sam was born.
Sam Alexis Woods splits time between her mother and father, who, as part of their divorce settlement, have joint custody of their children.