Part of the lore of Harry Potter and the Wizarding World explains that students at Hogwarts are grouped together into four "houses", which compete against each other throughout the academic year. The developers of Hogwarts Legacy have confirmed that players will not only be in houses but will also choose to which house they would like to belong during the sorting ceremony.
Gryffindor
Dormatory: Gryffindor Tower, directly north behind the clocktower
Element: Fire
Students sorted into this house tend to prefer chivalry, courage, determination, and nerve. Their common room is guarded by a painting lovingly referred to as "The Fat Lady", is draped in tapestries, and found in and around the Gryffindor Tower--which is located directly behind the clocktower on the south wall of the east campus just above the map of Argyllshire. Their fiery red house colors openly announce this house's affinity to the element of fire.
Hufflepuff
Dormatory: located underground beside and below the Great Hall
Element: Earth
Students sorted into this house tend to prefer dedication, fair play, hard work, loyalty, and patience. The common room for this house has the appearance of a badger's burrow. During the AutoDesk event on August 3rd, 2022, it was revealed that the common room has a vault-like door that requires a special knock to enter. The dorms for this house are located underground below the Great Stairwell and directly beside the kitchens. They are covered in earthtones.
Ravenclaw
Dormatory: Ravenclaw Tower, beside the gorge in the eastern complex of the school
Element: Air
Students sorted into this house tend to prefer wisdom and wit. Their common room is astronomy inspired, covered in blue carpet, and located in the Ravenclaw Tower. Both their mascot and position atop one of the tallest towers in the school reflect their house's relationship to air.
Slytherin
Dormatory: far below the main school in the "Dungeon Level", in part under the waters of the Black Lake
Element: Water
Students sorted into this house tend to prefer ambition, cunning, leadership, and resourcefulness. Their common room is built in the former basement dungeons and part of it actually extends under the Black Lake. Their windows are "wavy" to reflect this house's close relationship to water.
Dormatories
Each house has their own dormatory where the students can sleep and congregate. Each dormatory has one floo flame, one house chest collectable, and one secret entrance that only the students within that house are supposed to know about, though each entrance is flanked by themed braziers that are a dead giveaway to the observant.
House Cup and House Points
Despite being part of Harry Potter lore, it has been confirmed that the house cup and house points are not part of the game. The hourglasses, which are supposed to keep track of those points, are in the game and appear as they should next to the Great Hall. However, they are purely decorative.
Sorting Ceremony
Part of the story in Hogwarts Legacy is that the main character is joining Hogwarts late--becoming a fifth-year student. This is highly unusual. As a result, the student is actually alone on the stage during the sorting ceremony. As of January 12, 2023, it is unclear if this is because the main character has arrived later than everyone on the first day of school or if the main character has arrived on a later day altogether. As would be expected based on Harry Potter lore, there is a sorting hat who sorts the students into their houses.