I believe the term you're thinking of is licensed merchandise, a type of trademark license extended to third party products and services allowing them to use the likeness of a character or brand.
Licensed merchandise has been a major profit driver for entertainment companies for nearly a century, growing proportionate to the rise of mass entertainment in the 1930's and 40's. One of the biggest early examples of trademark licensing was mentioned in your original question, Mickey Mouse. Mickey Mouse exploded in popularity following the release of Steamboat Willie in November of 1928, ushering in a new Era of characters that transcend their original medium to achieve ubiquity on lunchboxes, tshirts, comic strips and watches.
Kay Kamen, an advertising man by trade, started negotiating merchandise agreements for animated characters in the early 1930's and was approached by Roy O. Disney about doing the same for Mickey. Infamously, Kay saw the opportunity this presented and decided to sew his life savings into his jacket for the trip to Los Angeles. He arrived at the meeting with a torn jacket, spread the money on the table and offered it to the Disney Brothers along with 50% revenue on future products.
Kay secured the rights for the next 20 years, and quickly began mass producing Mickey Mouse related products including the beloved and highly collectible Mickey Mouse wristwatch, the bestselling watch in america, a licensed product so popular it still exists today as an option on the apple iwatch. Kay was "a stickler for quality" and I would speculate that his intense focus on a quality product is what allowed for such broad consumer adoption, the relationship between merchant and consumer was build on a solid foundation of trust rarely seen in today's market. By 1948, Kay had generated over 100 million dollars in revenue and the market was still insatiable. Merchandisers took notice, and the trademark license industry was born.
Sources: "The disneyization of society" by Alan Bryman
"The Magic Kingdom: Walt Disney and the American way of life" by Steven Watts
"Walt Disney: The Triumph of the American Imagination" by Neal Gabler
And "Integrated Intellectual Asset Management" by Steve Manton