Aero Language is holder of all three authorizations. Aero Language has been certified when respective revision of Part-FCL has been in force naming organizations authorized for language proficiency assessments as LAB - Language Assessment Body. In March 2020, the Language Assessment Body - LAB name has been changed by an EASA to Language Testing Body - LTB. In fact, the requirements and certification basis are the same like the language assessment body - LAB.
Aero Language is using LAB and LTB in connection with language proficiency exams for EASA license holders only.
Due to the fact that Slovak republic is International Civil Aviation Organization member state, Aero Language is also authorized to provide language proficiency assessments in accordance with international ICAO standards as well. Due that fact, Aero Language is also TSP - Testing Service Provider. The abbreviation and name has been established by ICAO Doc 9835.
Aero Language is using TSP in connection with language proficiency exams for other than EASA license holders.
So in fact, all three abbreviations and names are correct when talking about Aero Language as an organization authorized to perform language proficiency assessments.