How do I distinguish dwarven clans from each other?

[Scalenex]

One point I've found to help always were random tables. By limiting creativity a bit you get a lot more creative and from randomness ideas tend to emerge.

Of course, you can roll or just pick.

The clan is proud of their:
1 - adhesion to traditions
2 - former victories
3 - riches
4 - famous ancestors
5 - great dwellings
6 - artifacts
7 - craftsmen
8 - pick one, roll for another

They are least proud of their (use bracketed option if the same number is rolled as above or if it fits better):
1 - weak adhesion to traditions (breach of tradition)
2 - former victories for the wrong reasons (current losses)
3 - lack of wealth (lost wealth)
4 - lack of famous ancestors (bad generation)
5 - poor dwellings (dwellings ruined by time or war)
6 - lack of artifacts (stolen artifacts)
7 - lack of craftsmen (craftsmen leaving for other clans)
8 - pick one, roll for another

Their patron (deity) is:
1 - 3 - one of major dwarven deity
4 - 6 - a minor dwarven deity
7 - 9 - a paragon (ascended ancestor)
10 - no patron
11 - a secret patron (non-dwarven deity)
12 - a secret patron (entity opposed to dwarves)

The leader is:
1 - unscrupulous, and will take any
2 - warmongering
3 - extremely orthodox
4 - paranoid
5 - greedy
6 - lustful
7 - a terrifying presence
8 - an extraordinary thinker
9 - a well-known artisan
10 - well-liked among his clan
11 - secret coward
12 - pick one, roll another, combine

Their leader was chosen as they are:
1 - charismatic
2 - great warrior
3 - great speaker
4 - son of a great paragon (ascended ancestor)
5 - strong of faith
6 - rich
7 - weak and easy to manipulate
8 - easily angered
9 - old and experienced
10 - skilled negotiator
11 - tough and resilient
12 - pick one, roll another, combine

Their clan inside is (roll 2d8, interpret):
1 - insidious
2 - mercenary
3 - loyal
4 - friendly
5 - formal
6 - hierarchical
7 - traditional
8 - hedonistic

(e.g. insidious/friendly = the clan hides its infighting behind a friendly mask, no open attacks are accepted but there is a daily dose of backstabbing and politicking; insidious/loyal = the clan has a lot infighting, but against outsiders they hold a common front)

These are just basic ideas, I can continue if you want. This can give you an easy way to create a bare-bones clans, which may have some reason to compete/hate each other. Example below.

Your charts are awesome! I need to modify them a bit to fit my campaign world. For instance, there is stuff I didn't mention the kalazotz which are gnome sized bat people who are frequently allied with the dwarves, though some dwarves view the kalazotz as loyal and true friends and others view them as smelly but useful little flying servants.

The reason why most dwarf non-combatants escaped the capture of their capital is that the kalazotz hid them in their nests, and the dwarves have not forgotten though that was centuries ago, and not all dwarves are equally happy to have kalazotz fluttering around.

I probably want to make a chart to see how well each clan gets along with kalazotz.

This is the one concept I came up before writing this post.

Shoemakers Clan Red Shaft Clan

During Meckelorn’s great exile, the Shoemaker Clan was usually too busy simply trying to survive to worry about making many shoes. At one point, the leader of the Shoemaker clan was locked in a deadly duel with an orc chieftain. This was a formal challenge, Warhammer style so a lot of dwarves and orcs were watching. The orc chieftain sundered his battle axe chopping the blade off the haft and the orcs cheered as their champion was about to win but then the dwarf took the broken shaft of his axe and stabbed it through the eye slit of the orc, demoralizing the other orcs and turning the tide of the battle.

The Shoemaker Clan thought this was so badass that they renamed themselves Clan Red Shaft. Their champion was blond as were a fair number of Shoemakers at the time. They took the sigil of a broken red axe on a gold field.

Clan Abehreh, sample kalazotz clan

Back when they were still called the Shoemaker Clan, the Abehreh clan of kalazotz was able to save the lives of many children of the Red Shaft Clan from goblins by hiding them in their nests. At some point, the leader of the Red Shafts decreed “From now until the ends of time, Clan Red Shaft and Clan Abehreh are allies! Let no outside enemy dare try to sunder our sacred bond!”

At the time, Clan Abehreh did not have a clan name, but they picked one so the Red Shafts could formally ally with them. Like most kalazotz clans that chose a name, they chose the surname of their most respected living members and kept it generations later.

Kalazotz are not as big on sigils like the dwarves are, but they have a few sigils they trot out on formal occasions. Clan Abehreh’s banner is a golden bat on a black field holding a small red axe with a crack in it, thus showing their alliance to the Red Shafts.

I'd also include something like a goal (for the clan, for the leader) and maybe organization of the clan (e.g. clan leader = total power, or there are advisors, councils, etc. - maybe linked to a size of the clan.

This is true. This youtube video on guidelines for creating interesting NPC suggests that every NPC have a weakness, a need, a desire, and an enemy (which may be a struggle and not a literal person or group).

For Stahlheim, the clans would probably act as quasi-cartels/guilds on a given trade. (Seafarers, gemcutters, crafters, ....)
That would influence their approach and outlook on society and power, as well as create conflict (mostly about pricing of transport, items and raw material...) .
If the PCs ally with one clan, they could maybe get special services/rare goods.

My original plan was to give Meckelorn powerful clan elders and comparatively weak guild leaders while Stahlheim was going to have powerful guild leaders and comparatively weak clan elders.

Though it would be more interesting and easier to keep track of if guilds and clans are tightly linked as opposed to them being loosely linked.