No, ganache doesn't have to be refridgerated, it keeps at room temperature below 75F for 2-3 days. The reason is because you scald the cream. It actually usually has a nicer finish if not refridgerated, it tends to lose a bit of its nice glossy sheen when refridgerated.
MOuse is right, if it is going to be somewhere warm, you will want to refridgerate it until serving time.
It looks like perhaps you tried to smooth the top with a spatula? The trick is to pour without smoothing. It is actually easier to get a smooth finish when you don't use buttercream under it.
Make certain you are not actually cooking your chocolate, but rather letting the hot cream melt it.
I cheat sometimes, if the top surface doesn't look smooth, I wait until it is set, reheat a bit of ganache and sort of drizzle or spoon a drizzled look to the top. It will make a pattern if you let it drip off the spoon onto a finished and cooled cake. Sometimes I just zigzag lines on top. Shh, don't tell, haha!
Your cake looks really nice though!
Hugs Squirrelly Cakes