1)
What kind of slave was Tziva?
1.
Radak: He was an Eved Kena'ani. 1
1
Radak: If so, how could David give to him Mefivoshes' property? What an Eved Kena'ani acquires belongs to his master! The king's command overrides this; he can take from one and give to another.
2)
Why did he say "ha'Atah Tziva"?
1.
Malbim: Were you freed? Freed slaves would change their name to a Jewish name, like converts do.