Fiberglassing 101
Covering that hole looks like an interesting project. Due to the curves involved, the simplest way to fiberglass it would probably be to get a sheet of formica or thin (THIN!) plywood to use as a mold to build against. Cover the inside with a smooth (SMOOTH!) sheet of plastic (the formica already is plastic) so the fiberglass doesn't stick to it, and screw it over the hole from the outside. Getting it to lie flat, with no buckles or bumps may be difficult. Do a dry run to see how hard it is. If it doesn't lie flat, you'll have to try a different method. If it does go on nicely, take it off and you can now roughen up the edges of the hole on the insides so it has some "tooth" for the new fiberglass to bond to. Then re-attach the mold over the hole. (You don't want the mold to be rough, but you need to make sure it works before proceeding.) Then cut out your fiberglass cloth and/or mat and go at it. After its set (wait until it is!!) you can remove the mold, fill the screwholes, sand the whole thing smooth, and figure out how to get the patch to match the color of your transom. Since this section of the transom is obvioiusly not structurally important (its a HOLE!), an easier fix might be to simply get a sheet of suitable material (formica might not last well outdoors, but it might work well enough; marine plywood could be mahogany and look really sharp varnished) that looks good to you, paint the name & hailing port on it, and screw or bolt it over the hole, and forget about fiberglassing. You could even avoid putting new screw or bolt holes in the transom by attaching the outside piece to a batten that overlapped the hole on the inside. A lot quicker, probably cheaper, and possibly better looking. Would work for me.