Tom, Dick, and Harry would work fine for an Earth-like world, but you still need to consider last names, unless you don't ever use them. There are also lots of options and resources when choosing names for your Earth characters and places, but what about those off-world stories. Now you can fall back on those same resources if your world happens to be an Earth colony, even if they have been long since cut off from Earth. But what about the completely fantastical, totally disconnected from Earth, world? Lets start by considering the history of names.
As I understand it, most names originated as a means of identifying a person by their job or status, but there can only be so many Carpenters, Smiths, and Carters, so they started attaching first names. Of course language and custom would have quite a bit to do with what names were chosen. Now how they decided on first, or given, names is unclear to me. Maybe some of them were just made up, maybe some of them were a bastardization of something they heard from another language as people started to travel, following the latest war or trying to run a trading route of one sort or another. Another thing to remember is that in many cultures, gender has an affect on the spelling of whatever name is chosen.
If your characters have never originated from Earth, there may be different customs involved in choosing names. For the names in my book, The Speed of Dreams, I went to a Dungeons & Dragons name list I have, and those with an apostrophe in the middle caught my eye, I morphed them some to fit the rhythm I wanted. I then decided on the custom that the clan name, or last name as we know it here, comes before the apostrophe. I got this idea from oriental names where the family name traditionally comes before the given name.
I've referred several times to my D&D list of names. It's extensive, including dwarven names as well as place names. It's great for sparking ideas when my mind draws a blank.
Now I've talked a lot about naming your characters, but character names isn't the only thing you need to consider. If your world is totally disconnected from Earth, it is highly unlikely they're going to give other things the same names we have. For the gist of your story, you can allow such things as buildings, mountains, and grass to exist, even trees can be called trees, but there's no reason to believe they'd be called Birch trees, or Spruce trees, and the flowers your hero is giving to his girl probably wouldn't be called Daisies or Roses, so you'll have to get creative all over again.
Naming these things, whatever you decide to name, isn't the only option. Who knows, there might even be cultures somewhere where a person has no name at all until he or she does something spectacular. In my soon to be released book, Half-Breed, in a culture where twins are common, identical twins were given the same name.
“When twins are born who are alike, it is common for them to share a name. It is thought that since the ancestors caused them to share a soul, it would be presumptuous of us to separate them by a name.”Choosing names can have so many layers of meaning, so have fun creating the foundation for your names. Even if you never explain what you've done, the detail will show, and it will also add life to your story.
What customs underlie your names?