Is there a formal name for an equation with multiple solutions?

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I saw that there is a related question for an equation with no solution, but I was curious about an equation with more than one solution.

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That's a perfectly good way to describe such equations.

Since you tagged the question with "quadratics", one calls the solutions of a quadratic equation the roots of the equation. The quadratic equation $x^2-1=0$ has two solutions (roots) at $x=-1, +1$.

Other equations like $\sin x = 0$ have an infinite number of solutions at $x=n\pi$, with $n$ equal to any integer.