It's up to you
There are two play styles (with regard to this question at least), with their own drawbacks and advantages.
The first is to keep the realms of the world (DM) and the player characters strictly separate. I use the term "Golden Box" to describe this. In Golden Box gameplay, the players cannot define anything about the world, including who an NPC does or does not know - that is in the purview of the DM. Similarly, the DM cannot define background for the player character.
The advantages to this method include not having to deal with this sort of question. The player only knows the NPC if you, the DM, say they do. The player can argue for it, usually backed up with a background, but in the end it's up to you.
The disadvantage to this is that there is very little flexibility, and the players can feel like they have very little agency over the game.
The second playstyle, which I will not name since the only name I know it by lacks general context, allows anyone to define anything, and it is only addressed if there is an issue or will be an issue if left unchecked.
The advantage to this kind of play is that the players usually have a lot more buy-in - they have created parts of the world. In situations where this is taken to its logical end, the players define the world, the npcs, and to an extent the antagonists. This can be a very satisfying way to play.
The disadvantage of this is primarily it gives 'that guy' a free pass for a long time (to wreck your plot), and it can make a game feel directionless.
These are extremes. You usually mix them when playing a game.
I would recommend, in your situation, that you tend towards the first. When the player declares something about the setting that gives them an advantage, have them justify it, or if the situation allows, to roll for it. Don't be afraid to say No, especially if the declaration the player makes is problematic.
Best Answer
The Dungeon Master's Guide describes how one can modify existing races or create new (playable) ones. Pp. 285-287, specifically.
However, there are more official playable races than just those in the Player's Handbook. You may want to take a look at What are the playable D&D races in 5e?
More broadly, the DMG is largely designed around the concept that D&D should not only allow you to create characters and adventures, but also spells, settings, races, new classes... your own game. I view it as a worked example of how to create an RPG in the D&D style. If you're looking for more than the Player's Handbook provides, the DMG likely gives some advice on how to get there.