When you're hitting a funny bone you're actually just hitting a nerve in your arm.
It's called a funny bone but it's a nerve that actually gets hit that causes the tingling sensation although you do also hit the bone in your arm.
It's very unlikely that you will actually cause any damage by hitting that nerve or your funny bone as you usually do not hit the bone or nerve too hard when you do hit it.
I've hit my funny bone as a kid and even as an adult and nothing bad has happened to me.
The doctor said there should be no damage or anything to worry about other than just feeling the tingling sensation for a bit.
That's why it's called a funny bone because it gives you a tingling sensation when you hit it.