Making the game free makes very little if any difference to the position here. There are two kinds of IP issues that could possibly be involved: copyright and trademark.
Note: both copyright and trademark are civil, not criminal issues (except in very limited circumstances which do not apply to the situation described in the question). You will not "face charges" but might possibly be sued. If you are asked to take down such a game and comply, this might end the matter, but if an IP holder claimed that damages had occurred before the game was taken down a suite might possibly still be brought against the developer.
Names, like titles and other short phrases, cannot be protected by copyright. As long as no other text from anyone else, and no images are copied or imitated, copyright is not infringed. This means that there are no copyright issues. Game mechanics and rules cannot be copyrighted, although the words of game rules can be.
Therefore, fair use which is a strictly US copyright legal concept, is not involved here. Neither is fair dealing, a somewhat similar legal concept from the UK and some commonwealth and European countries.
Here is the main issue for this situation. The names of individual Pokémon characters are probably (almost surely) protected as trademarks. That means you cannot use them to identify your game, or any other product or service, and you cannot use them to advertise or market your game. This is true even if the "selling price" is $0.
The use here does not seem to be nominative use, as you are not intending to refer to Pokémon or any of its variants. You are just reusing the names.
As long as you make it very clear that your game is not made by, nor in any way authorized or endorsed by the makers of Pokémon, this is probably not trademark infringement. But if the makers of Pokémon become aware of your game, they might well send you a cease and desist letter, and they might file a trademark infringement suit. Even if you were to win such a suit, as I think you might well do, it might be costly to defend.
Could you alter the names to ones you invent form yourself? That might save a lot of trouble and hassle. What is the value to you in reusing the well-known Pokémon names?