The core rules do not require a divine caster to speak his deity's name as part of the verbal component of casting a spell. It does require the divine caster to handle or manipulate in some way his holy symbol when the spell requires a Divine Focus as a material component.
So to answer your questions. No the cleric does not always need to handle his holy symbol to cast a spell, only when the spell requires a DF. And no the cleric never needs to speak his deity's name in order to cast a spell, not by the core rules.
So to answer your questions. No the cleric does not always need to handle his holy symbol to cast a spell, only when the spell requires a DF. And no the cleric never needs to speak his deity's name in order to cast a spell, not by the core rules.