Seeing as that last fic was the first time recently I’ve used the extended eldraeic name-format – or at least its most common version, since various cultures do it differently in some places and times, but this is the one that doubles as the modern International Standard – let’s talk about names and their parts a little:

Elyse Adae-ith-Atridae isil-Cyprium-ith-Avalae Erinlochos, ion-Tiryn, iel-Airin, mis-Eliéra-en-Palar

Elyse

Personal name/forename.  Works just like ours.  It’s often followed by a persona-identifier, which describes who you are relative to the entire identity described by the name, but at the time and place of “Slowly Awakening“, there’s only one of Elyse, and bothering to identify herself as “Elyse Prime” when there aren’t any parallel forks (“Elyse Secundus”, “Elyse Tertius”, etc.) or partial forks or other more complex multiplex identities in play would be less than pointful.

Adae-ith-Atridae

Family-of-descent name.  The format in question is House-ith-Lineage, where lineage is a subset of a House.  (If you think of them as septs of a clan, that’s not too far off.)  It can also be collapsed when they happen to be the same (the founding line of most of the Houses bears the same lineage name as the House name), in which case you can shorten, say, “Claves-ith-Claves” to just “Claves”, but in this case, being of the Atridae lineage of House Adae, Elyse needs to use the full format.

isil-Cyprium-ith-Avalae

Family-of-marriage name, i.e., the House and lineage name of one’s spouse’s family.  Same format, with an isil- prefix in front of it.  This arrangement is fully reciprocal in all cases, so, for example, her wife’s name is therefore “Calcíë Cyprium-ith-Avalae isil-Adae-ith-Atridae”.  (Those in marriages of other topologies than dyads would include all of their spice’s House-and-lineage names here – yes, this can get quite long.  There is also an alternate format for those special lengthy cases in which you give your marriage a name, in much the same way as other corporate entities have their own names.)

Erinlochos

Attributive name.  Covers the whole territory of formalized nicknames, titles, office-names, pen-names, and dozens of other things; most people have more than a few of them.  Most importantly, which one you choose to use is important because it tells people which of the people you are you are being right now, which is something that Imperial etiquette requires you to manage to a nicety.  You are supposed to keep the proper set of Chinese walls in your head and indicators in your speech such that on a family-owned tramp trader, for example, the same two people will always know whether they are having a conversation as captain-and-mate, or husband-and-wife, or business-partner-and-business-partner, etc., etc., and act accordingly.

Which they find much superior to accepting the confusion, fuzzy boundaries and fraternization regulations that we use to patch over the same set of issues.

ion-Tiryn
iel-Airin

Patronymic and matronymic.  (You can use full names, but you aren’t obliged to and usually don’t need to.)  Reasonably glosses as “fathered by Tiryn, mothered by Airin”, or “out of Airin by Tiryn”, depending on your personal taste.  An optional component if further identification is necessary than the rest of your name provides; customarily, women cite matronymics and men, patronymics – because that works best for identity-narrowing given that the custom is also that daughters are counted in their father’s House and lineage and sons in their mother’s – but either has the option of citing both, which is what Elyse does here.

mis-Eliéra-en-Palar

Loconymic.  Where you’re from – it’s actually where you consider yourself from, which is not necessarily where you live or where you were born or where you grew up (although it can be any of these; Elyse uses the last of those, although they live on Galíné, which is an outer-system gas giant moon in the same system).  In the original, ancient system, it would just have been mis-Location, but in these days in which the Empire sprawls over multiple worlds, it’s become mis-Planet-en-Location, just to make it easier for people to keep track.

There are, of course, plenty more optional components, but let’s worry about those when they come up, shall we?