The tower was originally named after the Scottish Enlightenment philosopher David Hume, who was an alumnus of the university.

In September 2020, in response to the Black Lives Matter movement, the university announced that they would be renaming the tower to 40 George Square.

The university stated that Hume's "comments on matters of race, though not uncommon at the time, rightly cause distress today.

[5] The structure of the tower is made from reinforced concrete with brick infill, and is clad with slabs of polished black slate and York sandstone.

[4] In 2006 Historic Scotland designated the building as category A listed, the highest category, stating the building is "one of the key monuments of Scottish Modernism", the architecture is of a "very high standard of design and execution" and the materials to be of "exceptional quality"[4] In 2014, the lower ground floor was renovated to create the DHT Hub, including teaching space, a café and a EUSA shop.