Why was the Abrahamic Prayer (Salat al-Ibrahimiyah) given this name, and not called the Muhammadan Prayer, even though in its formulation we invoke blessings upon the Prophet Muhammad (peace be upon him) before Abraham (peace be upon him)?

The reason for naming the Ibrahimiyyah prayer as such is not mentioned in the references. It is probable that the name came about to distinguish it from other forms of prayers upon the Prophet (peace be upon him) in which Ibrahim is not mentioned. The Prophet (peace be upon him) specifically mentioned Ibrahim (peace be upon him) in the Ibrahimiyyah prayer because he greeted his [the Prophet’s] nation on the night of Al-Mi'raj, while other prophets did not do so. Therefore, the Prophet (peace be upon him) commanded us to pray upon him in reciprocation for his kindness.