Recently, I've been wondering, from the 1950s to 1979, there was the Central Treaty Organization, but I don't know why it was named "Central". Do you mean the "center" of the Eurasian Continent?
The Central part of the naming of the Central Treaty Organization has to do with its association with other anti-communist leagues set up in that same time frame. You can see the association in a State Department publication here:
ORIGIN The Central Treaty Organization CENTO began, as did its earlier regional sister alliances- the North Atlantic Treaty Organization NATO in 1949 and the Southeast Asia Treaty Organization SEATO in 1954, as a response of free peoples to the threat from communism. The establishment of the alliance demonstrated the determination of the countries of the northern tier to preserve their independence by resisting Communist aggression or subversive penetration and by working together for stability In addition to membership in CENTO Turkey belongs to NATO and Pakistan is a member of SEATO
So Central Treaty Organization (CENTO) was associated with North Atlantic Treaty Organization (NATO) and Southeast Asian Treaty Organization (SEATO) to show the widespread geographic nature of the fight against the spread of communism. The consistent naming style is just there to provide a connection to the other organizations, therefore showing the unity in purpose of the organizations. This similarity in name choice is also noted in the Encyclopedia of the Cold War (emphasis mine):
Consequently, the Pact was renamed the Central Treaty Organization (Cento) on Aug 21, 1959, and its headquarters were removed from Baghdad to the Turkish capital Ankara. This name change highlighted the organizations similarities to the North Atlantic Treaty Organization (NATO) and the Southeast Asian Treaty Organization (SEATO), underscoring its cold war origins, and perhaps further undermining its credibility.
A footnote from another source The Arab Nationalist Advisor: Yusuf Yassin of Saudi Arabia,By Joseph A. Kéchichian, goes as far as pointing out the central positioning of this alliance between NATO and SAETO (emphasis mine):
CENTO was redefined as a conventional military alliance in the Cold War climate of the 1950s, and served as the central link in the chain of strategic defense pacts against the Soviet Union and it allies, established by the Western powers from the North Atlantic Treaty Organization (NATO) to the Southeast Asian Treaty Organization (SEATO).
They might have used Middle Eastern (METO?), but Central has a similar meaning to Middle, and could imply a wider, more expansive, less restrictive membership. It sounds better, is more inclusive, and accented its connection to the other organizations.