U2 is named after the first syllable in Yugi's name.
Yugi and Katsuya Jonouchi interacted their pets. Jonouchi's initially bullied U2, but they became friends afterwards.
Kujirada linked his virtual pet, Devil Master, with Jonouchi's pet and Anzu Mazaki's pet, Peachy and had it eat them. He later tried to let it eat U2, but U2 was able to change into a more powerful form, similar to how Yugi can change into Dark Yugi. This was due to the exchange of data it got from when it interacted with Jonouchi's pet, and how a person's virtual pet is supposed to "represent its owner". U2 then beat up Devil Master.
As the virtual pets usually only lived 21 days, Yugi says his goodbyes to U2 the night before he would perish, staying up all night to watch him until morning.
In the anime version, Honda's pet defeated Kujirada's. Haiyama later attacked Yugi. This causes Dark Yugi to emerge. Dark Yugi connected U2 to Haiyama's pet and U2 defeated it in the same fashion it defeated Kujirada's in the manga.