When was the K’abah built? By who? And why was it called the K’abah?

Shaykh ibnu Uthaymeen:

Allah says: {And (remember) when Ibrahim (Abraham) and (his son) Isma’eel (Ishmael) were raising the foundations of the House (the Ka’bah at Makkah)…} [Al-Baqara #127]. Therefore Ibrahim is the one who built the K’abah with the partaking of his son Isma’eel. It has come in some narrations that the K’abah was built in (Prophet) Adam’s time but it (later) collapsed then Ibrahim rebuilt it. And Allah knows best.

As for why it was called K’abah, because it is a squared shaped building and every squared shaped building which has four pillars is referred to as (كعبة) k’abah.

Fataawaa nur alaa ad-darb v.12 p.257