(Seek wider context here and here).
Those of Punthites
The Punthites, as a result of the codes rarely adopt names. If they need to identify themselves, their compatriots in their place of residence or work (often the same) will recognise them.
If a Punthite is compelled to travel, they identify themselves by their place of residence or work. Thus, one may refer to him or herself as Collective 101, Patrol 2442, Station 4077 or Ziggurat 17.
(Collective farms or Patrols will number in the thousands, Factories in the hundreds and Ziggurats in the tens).
Should further markers be needed, two coloured badges are chosen at random and pinned to the Punthite's tunic. Hence: RoadCrew 313 Grey-Mauve, Warehouse 890 Charcoal-Red, Battalion 290 Green-Green, &c.
Roll 2d20 for the coloured badges:
Those of the Qryth
The Qryth adopt names combining the world around them and abstract traits. Each Qryth is named individually at birth; they may later elect to re-name themselves. These names are (roughly) translated from the Qryth original.
The first part of each Qryth name is a quality of some description. It is generally a virtue, or at least desirable.
The second part of the name is an element of the periodic table, compound, alloy or material.
Thus, 'Strong Hydrogen' would roughly be the equivalent of John Smith or Jane Doe.
'Strong', 'Noble', 'Wise' 'Dextrous' or 'Prudent' might be used as first names; 'Hungry', 'Perfumed', 'Enrobed', 'Moist', 'Muscular', 'Royal' or 'Keen-Eyed' are either too temporary (it is easy to become un-hungry; one was not born wearing robes or scent), too fleshy or, in the case of 'Royal', connected to an institution. 'Observant' would be better than 'Keen-Eyed'. 'Pathetic', 'Psychotic' or 'Lewd' are technically correct but unlikely to be used by any well-adjusted Qryth (one might acceptably use 'Amorous' or 'Romantic' instead of 'Lewd' - the Qryth do not lack passion).
The periodic table of elements furnishes last names.
In accordance with the distance and mystery accorded to the Qryth, if an element has a name not ending in -ium, -on, -en, -ine, &c (IE, Iron, Gold, Copper, Silver, Lead, Mercury, Tin) consider using the Latin name (Ferrum, Aurum, Cuprum, Argentum, Plumbum, Hydrargyrum, Stannum).
An elemental name is considered more traditional, but this does not necessarily match to high social standing.
Common compounds such as 'Salt' render as Sodium-Chloride. I would suggest only using the simpler sort of chemical compounds, were one to use them at all.
Only a certains set of alloys and materials should be used in Qryth names. These materials should be inorganic - no leather or wood. A rule of thumb - if an engineer on Star Trek would commonly encounter it or recognise it or without using an Encyclopaedia, it can be used.
Thus, 'Steel', 'Diamond', 'Carbon-Fibre', 'Teflon', 'Transparent Aluminum', 'NeoSilk' or 'FauxWood' would work but 'Bakelite', 'Ivory', 'Parchment', 'Pewter', 'Brick', 'Corduroy' or 'Worsted' would not.
[As some of those names suggest, if you wish to use Space Age materials such as these, do.]
So, Qryth some names might include:
Learned Neon, Swift Lithium, Harmonious Stibium, Righteous Uranium, Ubiquitous Zinc, Just Bromine, Fierce Copper-Carbonate, Charitable Potassium-Permanganate, Ambitious Electrum, Curious Brass, Benevolent Cordite, Practical Nylon, Musical Leatherette.....
The Qryth are sufficiently advanced in terms of genealogy and record-keeping to maintain a knowledge of family lineages without the use of surnames. No Qryth will name their child the same thing as themselves.
Those of the Punthite that do not spend time with the Qryth think of their names as the equivalents of their own temporary identifiers.
Those of the Ka-Punth
The Ka-Punth, as they are not aliens or part of alien-dominated society have names closer to the rest of humanity. Whilst they are more likely to have absorbed names from other cultures than the Punthites or the Qryth, one may use names from the Ancient Near and Middle East.
Consider opening the Old Testament and leafing through it until you find a name you don't recognise. Other sources (such as this list) are available.