An epithet is an attachment to the name of a God or Goddess, used to indicate either a specific domain of the Deity, a specific origin myth or region from which the Deity came, or an entirely different entity, through either domain or origin.
An example; Aphrodite is the Goddess of love, beauty, pleasure, and procreation. She's either born from Zeus as His daughter or from the sea foam after Kronos castrated His father Ouranos. In the latter case, Aphrodite is the daughter of Ouranos, a Titan and a half-sister to Zeus. some historians claim Aphrodite was actually an imported Goddess (hence the different creation myths) and used to be a Goddess of war. Some of Aphrodite's epithets include:
Aphrodite Paphos - Aphrodite of Paphos
Aphrodite Diôniaia - Daughter of Dione, daughter of Zeus
Aphrodite Anadyomenê - Risen from the sea Aphrodite
Aphrodite Philommeides - Laughter-loving Aphrodite
Aphrodite Areia - Warlike Aphrodite
Epithets serve(d) either a ritualistic function or a literary on; hymns and chants are used in both aspects of Hellenismos and in both, destinctions are made between the various epithets of the Gods.
Within ritual, epithets are used out of respect, devotion a out of practicality. It's seen as respectful to address the Gods by their various names. It shows you are aware of the names of the Gods as well as the domains They influence. As for the practical; well, some Gods rule over a variety of domains. Zeus, for example guards travelers in His epithet of Zeus Xenios but is seen as the bringer of storm-clouds in his epithet of Zeus Ombrios. It's rather obvious, but getting rained upon is probably not what you were after when asking Zeus for aid on your journey.
Within poetry, epithets are used out of respect, as clarification and to add some flair to the poetry written. Certain forms of poetry relied on a set amount of syllables or words to work. Inserting and epithet helped fill the lines so they adhered to poetic rules. When reciting poetry, poets also added epithets to fill in a part of the poetry they had forgotten or to give them some time to remember the next line.
Within polytheism, epithets are of great interest. A short introduction on polytheism for those who are unsure of its meaning; there are two, or three, branches of polytheism; soft polytheism, hard polytheism and somewhere in the middle, is middle polytheism. All believe that Gods exist as actual beings and influence our lives. Soft polytheists believe that Gods with similar portfolios are the same God(dess). An example; Athena, Brighid, Sarasvati, Neith and Minerva rule the virtue of wisdom in their respective pantheons. For soft polytheists, this means they are the same Deity with different faces for each pantheon. Middle polytheists believe that some of these faces belong to the same Deity but definitely not all. Athena and Minerva are the same Goddesses but Brighid, Sarasvati and Neith are so different from each other, as well as from Athena and Minerva, that They can't be the same. Hard polytheists belief that each and every God and Goddess is a separate entity with His or her own powers, lives and story.
Epithets within polytheism pose a challenge; are all epithets different Gods or different faces of the same God(dess)? I belief Aphrodite Diôniaia and Aphrodite Anadyomenê are different Goddesses but the epithet Aphrodite Philommeides could be applied to both and is not a distinct Goddess. I have no set rule for this; it's a matter of feeling. Practically, this destination would mean I would say either this:
"Oh, blessed Aphrodite, Goddess of love and beauty, Aphrodite Diôniaia, Aphrodite Philommeides, I call on you, ruler over pleasure, oh, ever-laughing Goddess, now I struggle with love in my life. Aphrodite Diôniaia, Aphrodite Philommeides, daughter of Zeus the all-wise, if I have offered to you once, hear my plea and grant me aid."
"Oh, blessed Aphrodite, born from the foam of the sea, Aphrodite Anadyomenê, Aphrodite Philommeides, I call on you, protectress of those who take to the sea, oh, ever-laughing Goddess, now I journey over water to destinations at great distance. Aphrodite Anadyomenê, Aphrodite Philommeides, destined daughter of Ouranos, the primordial father, if I have offered to you once, hear my plea and grant me protection."
but I would never combine the two.
I'm fairly certain this destination is either completely unimportant, mildly important or critically important to other practitioners within Hellenismos; there is no set opinion in the Hellenic community on this as far, as I'm aware. Yet, if you are on this path, it might be something you want to get a clear opinion on.
For me, the use of epithets is important. They teach me a great deal about the Gods I worship and help focus my prayers and rituals. If you have an opinion on epithets, I would love to hear about it in the comments.