Thanks for your comments.
The two terms are used in different situations.

ichimei is used for polite situations and in written form:
Ex. Waitresses asking how many people are in your party.
Ex. Menus stating that a dinner course is for two people.
Ex. Hotel receptionists asking you how many people are staying.

hitori or hutari is for casual, colloquial situations:
Ex. “I went shopping alone” “Hitori de kaimono ni itta.”
Ex. “Why don’t the two of us go eat” “Hutari de gohan o tabeni ikou”

I hope that answers your question. Keep those comments coming!
Sachiko