Just a bit of feedback on this:
- I imagine this to benefit the most the endgame where you're in need of more tasks and goal to go after. Tierbased Rewards sound good, especially maybe a uniform at the end to proudly represent your faction if you wish to do so. Rewards should be unique so that each Faction has it's own appeal and arguments. Of course this would imply that you would need to change faction at will (you lose your rank and access when you do/you can belong to multiple), otherwise people are grounded on a choice of rewards they may later regret. Rewards can be TMs, access to certain spawn areas and customization. The daily/weekly quests can be done with randomized options, which could encourage people to visit even more places they wouldn't frequent otherwise anymore. There are a lot of opportunities to create options for endgame-players and reintroduce them more into the world again.
- I'll be harsh with my wording, but those names certainly sound like b-class guildnames that don't quite fit the tame, colorful and modern setting Pokemon plays in. Work with the lore, as you open your idea with the missing choice to Team Rocket, I would simply stay with the idea of joining a "Team Something"-Organization that try to achieve a goal lorewise. Some Teams have reasonable and fathomable goals like Team Plasma, they saw wrong in having Pokemon fighting for humans. Other teams are more controversial. You can definitely design a faction that is more good or evil, I'm sure that makes for an interesting choice for the player. Make sure those factions fit the lore and style of Pokemon.
-I don't see any point in deciding on the factions being enemies to each other if there aren't good reasons for it. You say there will be no factors gameplaywise that depict the hostile relationships, so why even bother? The only way I see this working is when you reward points for PvPing players of the other faction, so people are encouraged to PvP and find people of the another connection. Then again of course this could be abused by friends who just lose to each other on purpose. You gotta need to think of something, but please don't decide/define things that aren't reflected in the world/gameplay.