To determine the name of the ion \( NH_4^{+1} \), let's go through the steps systematically:
1. Recognize the chemical formula: The given ion is \( NH_4^{+1} \).
2. Identify the nature of the ions: The ion \( NH_4^{+1} \) is a polyatomic ion that contains one nitrogen (N) atom and four hydrogen (H) atoms.
3. Determine the charge: The given ion has a positive charge of +1.
4. Recall common polyatomic ions: One well-known polyatomic ion with the formula \( NH_4^{+1} \) is the ammonium ion.
Thus, the name of the ion \( NH_4^{+1} \) is ammonium.
Therefore, the correct answer is:
ammonium.