What you need to do is put down an NPC group. In this case it needs to be one of the enemy groups, so if its a Federation mission, use anything but Federation groups, if its a KDF mission, anything but Klingon, Orion, Nausicaan, etc.
If you want just one ship to spawn, use a cruiser or battleship group. The groups spawn more ships if there are more players in the group, but I think (just a guess) that most people play solo, so cruisers and battleship groups will just spawn one ship, the battleship one being tougher and slower.
Now, there are a couple ways to put the name on that one ship. First is to zoom in on the group in the map till you can see the individual red dots, click on these, you should see a field with the ship name that you can change. The other way is to look at the object list on the left-hand side and find the entry for that NPC group, click the triangle to expand it, then it will show you each of the NPCs that may spawn from that group, click on them and you can rename them just like in the first method.
On that screen there will also be a button "Click to Select Costume" or something similar, this will let you select what the NPC ship will look like. Keep in mind that the NPC will still fight like whatever it was originally. So if you put down a Klingon NPC group and reskin them as Federation ships, they will still have Klingon weapons and abilities.
Lastly, since you want to be sure that the named ship spawns and sometimes it can be tough to know which NPC in a group will spawn, I recommend renaming and reskinning every NPC in the group the same.