The opposite process, the loss of a sound from the beginning of a word, is called apheresis or aphesis.

Complex blending, with both apocope and aphesis:

Most etymologists believe it to be the product of aphesis, the process by which we clip unaccented vowel syllables off a word's stem.

Blending with either apocope or aphesis:

Other words were formed through aphesis (from "apanar" was derived panar; from "otana," tana).

Article by Martin Gansten from Lund University - Balbillus and the Method of aphesis (July 2012)

Most modern biblical scholars, however, regard the name as a reference to the Amorites, the initial a via aphesis; the name is thus interpreted as meaning land of the Amorites.

At a recent meeting of the Aphesis group, collected information was presented which requires further analysis, e.g. the incidence of TRALI (transfusion related acute lung injury) requires calculation.