PUBG ranks are determined by the amount of MMR points that players have. In order to get ranked you will have to play 10 games. Before that moment you will belong to Unranked group. Keep in mind that MMR can be not only increased, but decreased as well. PUBG rank is different for each game mode.
All 8 PUBG ranks and the amount of MMR points you have to earn:
BronzeMMR points: 1 – 1,399
SilverMMR points: 1,400 – 1,499
MMR points: 1,500 – 1,599
MMR points: 1,600 – 1,699
MMR points: 1,700 – 1,799
MMR points: 1,800 – 1,899
MMR points: 1,900 – 1,999
MMR points: 2,000
This rank is only available for top 100 players of that specific in-game mode.