What is the name of the mode where you control a team over multiple seasons?

The mode where you control a team over multiple seasons is Franchise mode. It turns a single Madden game into a long-term management experience built around roster decisions, competition, and team development.

Franchise mode was introduced in Madden NFL 99, released in 1998. Players could guide a team through as many as 15 seasons, while handling activities beyond individual games, including trades, free-agent signings, releases, drafts, and season scheduling. Later editions expanded the concept with owner responsibilities, online leagues, scouting systems, salary management, and deeper player progression.

Play Now is designed for individual exhibition games, not a continuing sports-management campaign. Ultimate Team focuses on assembling a customized roster from collectible player items, while Superstar mode centers on an individual player or career. Those modes can involve progression, but Franchise mode is the canonical answer when the defining feature is managing one team across multiple seasons.