The phonon Raman spectra of Bi2Sr2Ca1-xYxCu2O8+d (x=0-1) have been investigated in a number of well-defined single-crystal and polycrystalline samples. From the polarization and Y-doping dependence, and from a comparison with previous reports on Bi-based cuprates, we identify the (6A(1g)+1B(1g)) symmetry modes that are Raman allowed within the ideal body-centered-tetragonal unit cell. A large number of extra ''disorder-induced'' phonon bands are observed in the ab-plane polarized spectra. In contrast to most previous reports, we argue that the c-axis polarized phonon band around 629 cm(-1) is due to the O(2)(Sr)A(1g) vibration, while the exclusively ab-plane polarized band around 463 cm(-1) is induced by the O(3)(Bi)A(1g) vibration. With increasing Y doping we find that the vibrational modes involving atoms in the CuO2 planes rapidly increase in intensity as a result of the reduced metallic screening in the hole-depleted Y-doped samples. We also find that Y substitution gives rise to a substantial hardening of the O(1)(Cu)A(1g) and B-1g phonons by similar to 40 cm(-1), whereas the O(2)(Sr)A(1g) phonon is found to soften by similar to 20 cm(-1), when x increases from 0 to 1. The phonon frequency changes can be explained by the ''internal pressure'' induced by the decrease in the average Ca/Y ion size and an additional ''charge-transfer'' induced by the change in the Cu and Bi valences with Y doping.