International civil aviation is governed by the Chicago Convention. Annex 10 of the Convention deals with aeronautical telecommunication and contains detailed regulations in relation to all radio communication matters, including the use of call signs by aircraft. Call signs are unique identifiers used by an aircraft in radio communications, in compliance with international and national rules. It is not unusual for an aircraft to use different call signs for different flights.
The aircraft referred to by the Deputy in parliamentary question number 593 of 21 February 2017 was operated by Miami Air International. The aircraft arrived in Shannon using the BSK call sign used by Miami Air and departed Shannon using the CMB call sign for the next leg of its journey. The CMB call sign is used by civil aircraft on charter to the US military.
Such changes of call sign are not unusual and are permissible under international rules. I am not aware that such changes cause any difficulties.