Elezen Nobility and Surnames
(Blue text is speculation and not explicitly canon)
This post doesn't list every known elezen noble. I will update as I remember/discover them. If any large lore revelations are had I'll create a whole new post with revised & updated information.
King Galvanth / Galvanth the Dominator - Former king of Gelmorra (Tam-Tara Deepcroft, the Mindflayer is using him as a host)
King Thordan - the original king of Ishgard and the last.
Prince Haldrath - Thordan's son.
de Dzemael (Dzemael Darkhold fame)
Grinnaux the Bull is the most notable member of this house. Because he is a member of the Heavens' Ward he is unable to inherit anything and cannot have children.
Stephanivien (MCH quests)
Laniaitte (MSQ camp cloudtop)
Francel (MSQ / Firmament Quests)
There is a schism between the high houses and the other nobles of Ishgard. Although nobles, some of the members of the High Houses look down on the lesser houses as little better than commoners. Still there's an obvious divide between being a lesser noble and an actual commoner. Lesser nobles are still part of high society.
de Valentione - Second to only the High Houses. Interestingly enough the next in line for head of house is a woman, Lisette. In fact it seems the family is matrilineal unlike most of the other houses (Valentine's Day Seasonal Event Quests).
de Caulignont - Ystride and Rielle's house (DRK quests). Interestingly enough Ystride's husband seems to have taken her surname. Or at least Ystride kept her surname and it legally passed on to Rielle.
de Chevraudan - Ser Adelphel's family. A lesser house.
de Jaimberd - Ser Noudenet's family. Barons from Coerthas central lowlands. May have been struggling financially as they sent away Noudenet to Saint Endalim's to have one less mouth to feed.
de Lasserant - Drillemont's surname.
de Faurechort - A lower house, several centuries ago a daughter of the house married into House Dzemael.
de Jervaint - Laurisse is the only surviving member of the fallen house and aspires to be a knight and bring glory back to her house (BSM Quests).
de Thelomaire - Jantellot is the only known member. He's the leader of the Convictors which are comprised of "petty nobles and penniless commoners".
de Vimaroix - Heustienne's house that she was adopted into (DRG Quests). Current head of house is Montorgains.
Unknown house name - Guillefresne's and Jandelaine's house whose surname is unmentioned. According to Guillefresne we aren't likely to know them. However they are connected to House Dzemael. Both are duskwights.
Distinguished Gridanians - A statement made by a Wood wailer by the name of Severaint. He guards a section of Gridanian unacessable to the player and warns you off, stating commoners may not enter.
d'Arlendre - Mentioned name for a staff description. Specifically referred to "House d'Arlendre". Knowing French grammar conventions the d' is just de. Notable member is lady Cliaie, a former prisoner in Toto-Rak (pre ARR)
Lhorulgois - (BRD quests) Seemingly Gridanian nobles. Notable member is Vainchelon, a general during the autumn war and mentioned to be a lord. Current member is Nourval.
Dartancours - Once one of the oldest and most notable nobles of Gridania. The most notable member being Lady Amandine (Haukke Manor).
Note: I've seen people call her a duskwight. She was a duskwight but that has since been changed to her being wildwood. Additionally were claims that she's Ishgardian. That was fan speculation due to the lack of information about Gridanian nobility other than a few in game comments strewn about in side quests and item descriptions.
de Nevelle - Duskwights. Specifically the two known members refer to themselves as duskwights. It is possible they live outside of the Black Shroud, however they appear to be noble due to the use of 'de'. This implies there are still duskwight nobility running around.
Notable members are Rolandaix and Irelle who are seen studying the exposed Gelmorran ruins. Their ancestor Jean de Nevelle was part of the crew who discovered La Noscea and helped settle it. La Noscea taking the name of a crewmate who perished.
Unclear whether nobility or social class. At the very least they are all 'upper'.
Mena & Inik - Two Gelmorran noble houses. We only see the servants (who use midlander male models).
la Treaumaille - The surname of Hermonost of the Heavens' Ward. His family were merchants and only he possesses the 'de' in front of his surname.
Guy la Thagran - Another member of the expedition who discovered la Noscea.
la Noscea - the guy, not the island. We know he died two days before the Galadion made it to said la Noscea
Menenius sas Lanatius - His mother was a widowed Landisan noble woman whom his adopted father married for political reasons. What his mother's maiden name (or previous husband's name) is unknown. Similarly is if Landis elezen used to 'de'.
Urth - Was an elezen with some connection to Odin. She seemed to be of some import to her people (there's a location named after her and her slaying by Odin is significant). Referred to as Lady Urth. Unknown whether she was noble or just respected and what culture she came from
De is well established to denote a noble house. La is slightly unclear as while there is three uses of it I found, only one mentions the family's social standing. If I had to speculate it seems 'la' may be used for non titled upper class/the wealthy.
Knights of the Heavens' Ward are given 'de' before their surnames regardless of their previous circumstances. Although they are not supposed to have children so the noble status is not inherited.
What about ak, the prefix before the ak-Mena and ak-Inik varlet?
Ak is a prefix for deceased members of a Gelmorran house. So ak-Mena Varlet is a shorter way of saying "deceased varlet of House Mena".
Noble titles (and who uses them)
Heads of lower noble houses
Jannequinard de Durendaire
Presumably some non inheriting members of High Houses may use this title, perhaps if they have some form of higher responsibility (see Jannequinard).
Noudenet de Jaimberd's father (From somewhere in Coerthas central lowlands).
Hilda Ware's father is/was a baron.
Janetellot de Thelomaire - a hyur Convictor mentions wanting to catch the respect of a baron and earning fame. He may be talking in general or about their leader.
The High Houses seem to follow the rule of the oldest true born son being heir, with few exceptions. Emanellain casually mentions he's set to inherit nothing and live lavishly off Artoirel. Durendaire is suffering a succession crisis since Charlemend's son "died" and it's speculated whether he'll sire another heir or choose a less than ideal one (note: Jannequinard is his nephew).
Other houses are different. Valentione seeming to choose the oldest daughter and others making no discernment between sons or daughters inheriting.
The distinction between these two concepts seem to be blurry.
I would argue that wards keep their birth surname and are not heirs but may be treated as nearly the same as true born children. Adopted children take their adoptive parents surname and may even inherit, they're on the same standing as blood children but their blood status may still leave them under the scrutiny of the other nobles
The High Houses seem less likely to use adoption as a means to produce heirs. This might even be one of the speculated "less ideal" options that Charlemend may resort to.
Additional Information on surnames
Not all elezen surnames appear to be taken from masculine forenames, some appear to be feminine forenanes. However there is overlap in the naming conventions between the sexes so they could all be male names. (Some male names have feminine endings and some female names have masculine endings.
Also surnames are not always inherited patrilinealy, see the Valentione's and Caulignont's above.
That means you can probably have an elezen with a feminine sounding surname and/or having inherited their mother's surname instead. Neither are against lore and have lore that supports it.
You can also easily have an Ishgardian duskwight as well. The lore only supports Ishgardians with duskwight features, even those with ties to the High Houses.
Go ahead and make a matriarchal matrilineal duskwight noble house!