It's usually called a hawse pipe or chain pipe. There are a few different ways to seal them. One is to have a cap that fastens over the opening that is held in place by a screw coming up the hawse pipe. Another is using a fast pin to hold the existing cap in place. Another is to use an expandable plug to fill the hole.
With an oval shaped one, I would probably recommend using a fast pin to hold the cover in place. Drill a 1/4" hole through the side of the cap and the hawse pipe itself and insert a 1/4" fast pin.
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at this time, if further ideas need exploring. I am trying to avoid the installation of such a pipe, which I used to call a "hawse pipe", but now call a chain pipe or a chain fall because I don't carry my anchor, destroyer style, in a notch on the side of the bow from which you can also run "hawsers". (I find the more particular I am about nautical terminology, the less ambiguity is created, but that's just me.)
One idea I know of is to put even a one-inch high collar around the hole in the deck. This should reduce the water coming inside somewhat as the water naturally sloshing on deck from spray can't find that hole and use it as a drain.
At sea, I would stow my anchors and perhaps my chain (I keep it in an anchor well) below to get the weight off the end and to reduce stress on my bowsprit. It is also not inconceivable that beating into heavy seas could chafe the light lashings that are usually sufficient to keep the shanks in place entirely through and I could have a "surprise deployment". If I was in coastal or otherwise thin waters (like in the typically rough water over an oceanic seamount), this could be quite destructive were I going at a good clip.
So while it's more work, I would shift my anchors below into the forepeak. I would also bag them, because I have found that even on Lake Ontario, anchors can damage the paint just through moving a little bit a few thousand times on the same spots.
"Chafe is the enemy" isn't just about lines and sails, I am learning.