Let $f(n) = O(g(n))$, but not $f(n) = o(g(n))$. That's a nice property, because it means that we cannot replace $g(n)$ with a substantially smaller function. Is there a name for this choice of $g(n)$? Obviously this covers more cases than just $f(n) = \Theta (g(n))$. It requires the existence of $c > 0$ such that $f(n)\geq cg(n)$ for infinitely many $n$. 
Name for function in big O but not in little o?
terminology;asymptotics