Attachment Contrary to popular belief, Rare's name was never "Rareware", even before the Microsoft buyout in 2002. On an old Rare Scribes post dated June 19, 2000, it was confirmed that the name "Rareware" refers to the company's products, not the company itself. It's essentially a portmanteau of "Rare" and "Software". The company itself was always internally named Rare Limited.
person Dinoman96 calendar_month November 24, 2023
Rare Scribes - June 19, 2020:

Example of official Nintendo website referring to them as Rare Ltd. (Banjo-Tooie game page):
One of the prototype games Rare had created to test programming for the Kinect had the player control a seagull, and attempt to poo on passers by.
subdirectory_arrow_right Ultimate Play the Game (Company)
Attachment During their time as "Ultimate Play the Game", Rare were known for having minimal marketing to the point of not even releasing screenshots in magazines, and having print advertisements comprise of game logos and nothing else.
subdirectory_arrow_right Kinect Sports (Game), Kinect Sports (Collection)
A common internet rumor, typically pushed by Nintendo fans upset over rival console manufacturer Microsoft's purchase of former Nintendo collaborator Rare, is that Kinect Sports and Kinect Sports: Season Two were mandated by Microsoft, and were not something that employees of Rare wanted to work on. According to Yooka-Laylee creative lead Gavin Price, this was not true, claiming:

"Phil Spencer taking the mantle of Xbox is one of the best things that could have happened for Rare. Because he’s always said to people at Rare [as general manager of Microsoft Studios], ‘Do what you want to do and we’ll back you,’ and he’s always stayed true to his word in that regard. It was people in Rare’s management at the time who said: ‘Well, Kinect is a great opportunity for the studio – go all in on it.’ So when executives at Microsoft see that the management team are passionate about doing that, they back them. Microsoft to their credit did that, and perhaps the story online isn’t quite reflective of the truth."
Grant Kirkhope, music composer for Rare at the time, reused songs he had composed for Rare's unreleased game Project: Dream for several other titles, including Banjo-Kazooie, Banjo-Tooie, Donkey Kong 64 and Viva Piñata.
According to Chris Seavor (creator of Conker's Bad Fur Day), Rare wanted to explore 'amiibo styled things' way back during the days of the Nintendo 64. Rare even made figures of two of their characters for an unproduced fantasy video game called Urchin. The idea went nowhere with Rare and Nintendo at the time. Later, Nintendo decided to introduce the concept of Amiibos for the Nintendo Wii U and 3DS on June 10, 2014.
When Microsoft had acquired Rare, they'd decided to keep their in-house Game Boy team as Microsoft had no intentions of entering the handheld market. Rare would continue to develop games for the Game Boy Advance and Nintendo DS. Microsoft themselves had also released other games on rival platforrms.
Attachment The company started out as Ultimate Play the Game (often shortened to Ultimate), making games for the popular 8-bit home computers of the time.
According to former Rareware employee Chris Seavor, when the company was purchased by Microsoft, a number of the Microsoft executives thought that they had the rights to Donkey Kong until Rare corrected them.