In the lobby there are tags with numbers on against some player names - what are they?
There are two types of adornments that can go next to a player's name: Generation markers and Rank markers.
Once you reach Level 50, you can "Regenerate" upon completing certain challenges, like achieving a certain number of kills with a particular weapon or winning a set number of matches in a particular mode. You lose all unlocks, upgrades, and achievements (you keep your Burn Cards, though), and are set to Level 1, but are given a bonus XP modifier and a tag next to your name indicating which regeneration you're now on. This is akin to "Prestiging" in Call of Duty. There are 10 Regeneration levels.
If you choose to activate your Rank Chip, your Regeneration marker is replaced by a Rank Marker. This starts at Bronze 1, as denoted by a worn, bronze-colored marker with the Roman numeral "I", and increases as you gain rank points. There are five levels in each tier, labelled "I-V". There are also five tiers: Bronze, Silver, Gold, Platinum, and Diamond.
If a player is not using a Rank Chip and is Generation 1, there will be no adornment next to that player's name.