The United Nations records Tanzania's date of admission as 14-12-1961, and Zanzibar merged with Tanganyika to form the United Republic
Background
The World Bank and United Nations items elsewhere in today's country section all name the country by its treaty title, the United Republic of Tanzania, and this is where that title comes from.
The United Nations list of member states records for the United Republic of Tanzania a Date of Admission of 14-12-1961.
The United Nations record of growth in membership states that on 26 April 1964, Zanzibar merged with Tanganyika to become the United Republic of Tanzania.
Tanganyika joined the United Nations in 1961 and Zanzibar joined in 1963, each under its own name.
The Commonwealth records that the United Republic of Tanzania joined the Commonwealth in 1961, after independence from Britain, and that the country includes the island of Zanzibar.
In plain words
Tanganyika Tanganyika — The mainland territory that became independent in 1961 and later united with Zanzibar.