Nitrogen trihydride is one nitrogen and three hydrogens because nitrogen can have five valance electrons sharing with the three hydrogen atoms to form a full octet. And each hydrogen has a full duet. This could be represented with Lewis dot models to show sharing of electrons.
This represents covalent bonding due to the type of atoms (nonmetal-nonmetal) and naming system (prefix system).
This molecule is also known as ammonia from Greek times.