What class is the ship?
Might be better to choose knowing if she's an explorer, escort, cruiser, surveyor, etc.
I second this. You're not going to want to name a science or research vessel, after some mythological god of war, and you'll likely not want to name a warship after an explorer or famous scientist.
So the ships name shouldn't be arbitrary and picked at random. If it's a canon ship class, then look at the names that already exist and try to pick something that follows the naming convention already is place.
If the ship is of a class that is non-cannon and one that you've created yourself, then you can set your own naming convention...naming ships after moons in a certain solar system or rivers/lakes on Earth.
If someone else created the ship, ask them if they had some sort of naming convention in place. They may be able to provide you with a list on names to choose from.
And thirdly, you may want to consider what role the name will play in relation to the series itself. If your series is focused on the exploits of a doctor or some group of scientists, then you should pick something that conveys that, as it may end up being used as a title in some way.
For example, if creating a medical focused series, you could go with Hippocrates (as in the Hippocratic Oath) and call the series Star Trek: Hippocrates.
So if you picked the name Reliance, then it would be easy to just name the series, Star Trek: Reliance.