"I know that epithets were used to talk about specific aspects of a deity, but were there any instances where an epithet would be used in order to avoid using a deity's name? Say out of respect or something?"

Absolutely! Ploutōn (Πλουτων), as an epithet for Hades, is perhaps one of the most famous ones. The epithet eventually became an alternate name and then a parallel God. In ancient Hellenic religion and myth, Ploutōn represents a more positive concept of the God who presides over the afterlife. The name Ploutōn came into widespread usage with the Eleusinian Mysteries, in which Ploutōn was venerated as a stern ruler but the loving husband of Persephone. The couple received souls in the afterlife, and are invoked together in religious inscriptions. Hades by contrast had few temples and religious practices associated with Him, and was portrayed as the dark and violent abductor of Persephone.

Ploutōn and Hades came to differ in character, but they are not distinct figures and share their  mythology. Ploutōn as the name of the ruler of the underworld first appears in Hellenic literature of the Classical period, in the works of the Athenian playwrights and of the philosopher Plato, who is the major Hellenic source on its significance. Under the name Ploutōn, the God appears in other myths in a secondary role, mostly as the possessor of a quest-object, and especially in the descent of Orpheus or other heroes to the underworld.

In general, Khthonic--Underworld--deities have epithets that make them less scary and more helpful to humanity, and then there are Ouranic deities who have darker epithets. Zeus Meilichios (Ζεύς Μειλίχιος, the Kindly One) is a Khthonic epithet of Zeus, who receives only night-time sacrifices, and only by way of a holókaustos. Zeus seems to have adopted the Meilichios epithet from an older Khthonic serpent daímōn or Theos. He is--like the Erinyes and Alastôr--an avenger of blood feuds between families. Yet, unlike the others, Zeus Meilichios is also a purifier. When someone avenged the murder of a family member by killing the killer--or even someone else from that family line--they could petition Zeus Meilichios with a holókaustos of sheep (ram, or another four-legged creature would also suffice) and be cleansed of miasma caused by this murder. The skin from the sacrifice may have been saved for purification rites in the Pompaia.

Epithets are ways to speak to only certain parts of a deity--to address just a fraction of Them and receive only a little bit of Their attention. Some Gods are too great--or our actions too shameful--to engage the deity fully and then we make use of epithets. Out of respect, out of fear, or out of practicality.