There are no, concrete RAW monster knowledge checks in 5e
The PHB, MM, and DMG do not mention anything like a monster knowledge check as existed in previous editions. Tied with that is the fact that monster types are not directly tied to skills. As such I can only offer guidelines based on my own experiences with 4e and 5e and what I have done as a GM.
Go with what makes sense for the creature/creature type.
Beasts for example might allow either the nature or survival skill to be applied to a knowledge check, arcana for any constructs or monsters from other planes, religion for demons, devils, and angels etc.
Apply the standard DC check ratio as laid out in all of the books and pdfs.
- 10 Easy
- 15 Medium
- 20 Hard
- 25 Very Hard
Passing the easy check lets the players know/guess the monster and its type. Medium Allows the players to know the types of attacks it will make (melee vs ranged and can it cast spells). Hard also lets the know resistances or immunities. Finally with a Very Hard DC met the players can look at the actual creature statblock. You can even restrict the Very Hard DC to only be given out to a player who is trained in the skill you are asking for.
That said, are monster knowledge checks required?
Its entirely possible for you as the DM to simply state whether or not a PC would know about a monster based on their backgrounds and experiences. You would need to discuss this option with players, but 5e's rules-lite narrative leanings would lend itself well to this so long as your players were on board with it.