Most of the methods of identifying wolf personalities are accurate, but not all of the information here will be useful to your specific playthroughs and you might prefer one thing to another, so in the end, it's up to you how you pick your mate!

In Wolf Quest: Anniversary Edition, there are 6 total personality traits that range on a six-way axis.

Cautious ↔ Bold
Loner ↔ Social
Lazy ↔ Energetic

These traits are randomized in roaming groups of AI dispersal wolves, which means that any dispersal with the potential to be your mate can have a unique set of defining traits that will determine both their usefulness and survivability in your playthrough.
Additionally, you can choose your own wolf's personality traits using sliders in Wolf Creation.

The personality traits you choose for your wolf may contribute to what personalities your pups inherit, so choose wisely! It's likely that personality traits will affect how pups help out when they're older (in the Saga update somewhere down the line).

If you're new or inexperienced, you may not notice right away which wolf behaviors are personality traits. You may even be inclined to think that certain behaviors are bugs or errors in programming.
However, there are several behaviors that are somewhat unique to each personality trait, and here's how you can identify them!

• Cautious wolves will run several feet away from the player during courtship, if you approach them immediately before convincing them to get to know you.
  
• Cautious wolves will lock on to prey animals, but will not sprint. They'll wait until you grab onto prey before grabbing on themselves.
  
• In stranger wolf territory, cautious wolves won't be doing a lot of fighting with stranger wolves if you pursue them.
  
• Cautious wolves may be quicker to back out of a confrontation, and may be more afraid of predators, like grizzlies & cougars.
  
• Cautious wolves may be less likely to attack prey with high health; alternatively, cautious wolves with low health may hesitate to attack prey at all.
  
• Cautious pups may be more likely to hide on their own when they're threatened.

• Bold wolves may only take a few steps back from the player during courtship, if you approach them immediately before convincing them to get to know you.
  
• Bold wolves will dart ahead and latch onto prey without waiting for you to initiate the attack.
  
• In stranger wolf territory, bold wolves will relentlessly pursue and attack stranger wolves until you have to flee to make them stop.
  
• Bold wolves may take longer to back out of a confrontation, and may be less afraid of predators, like grizzlies & cougars.
  
• Bold wolves may be more likely to attack prey with high health; alternatively, bold wolves with low health may still attack prey.
  
• Bold wolves may frequently howl unprompted.
  
• Bold pups are more likely to wander/leave the safety of their hiding spots, or even face a threat head-on instead of hiding.

• Loners will be less likely to eat with the pack. (They may grab a meat chunk and carry it elsewhere to eat.)
  
• Loners will be less inclined to howl, especially at the home site; they will also be less likely to autonomously initiate interactions.
  
• Loners may keep their distance when sleeping or resting.
  
• Loners will scavenge or hunt for themselves when they need to, and are capable of bringing down prey on their own.
  
• Loners will prefer to be stay-at-home parents with pups while you're out doing other things.
  
• Loner pups tend to stay farther away from the pack, and hesitate to play with their siblings.

• During courtship, social wolves will frequently emote to the player much more than loners.
  
• Social wolves will tend to eat, sleep, and rest near the pack.
  
• Social wolves may be more inclined to howl with you.
  
• Social wolves do not like to hunt alone, preferring to follow you and join in on excursions. They may go hungry without food being provided to them.
  
• Social pups generally stay with the pack and will often initiate play with their siblings.

• During courtship (and most other times), lazy wolves may not move very much. They may sit or lie down frequently when idle.
  
• Lazy wolves may participate only a little, or not at all, during hunts or confrontations. They'll fall behind or run around not doing much when you initiate something.
  
• Lazy wolves will not automatically join you or send the pups into the den when you leave the area; they may need to be told to follow you.
  
• Lazy wolves, if participating in a hunt, might only bite prey once and let go before doing much (if any) damage.
  
• Lazy wolves are less inclined to feed pups, pick them up when they stray too far from the den, or find them if they get lost.
  
• Lazy pups may sit or lie down more often when they're idle.

• During courtship (and most other times), energetic wolves will not stand idle for long. They're typically moving or doing something.
  
• Energetic wolves may dart ahead and latch on to prey without waiting for you to initiate the attack.
  
• Energetic wolves are more likely to participate in a hunt or confrontation, and won't usually hesitate to join you.
  
• During hunts, energetic wolves may bite multiple times, and hold on to prey until they get kicked off.
  
• Energetic wolves are more inclined to feed pups when they're hungry, pick them up when they stray too far from the den, and look for them when they get lost.
  
• Energetic pups are more likely to chase their tails, and expend extra energy in play.

Because these traits appear on an axis, and it's not strictly one or the other in many cases, some wolves may have "inbetweens" where they exhibit some behaviors from either end of the spectrum.

Each personality trait comes with its benefits and downfalls. Some are highly desired, because it entails a simpler or 'safer' playthrough with more downtime, even on harder difficulties. Others are less desired due to the challenge they impose on the player, depending on preference.

Depending on how you want to structure your playthrough, you might prefer a mate with certain personality traits.

For example, if you want a playthrough that allows you downtime to loaf around with pups, and you don't want to worry so much about constant movement and chores (in other words, if you want to be a little bit lazy), you might want your mate to be Cautious, Energetic, and a Loner.
These wolves are capable of managing their own needs, so won't demand constant attention from you regarding chores like territory defense or intensive hunting.
Basically, they can survive without you for a while.

Although, if you would prefer a mate that stays at home and does all the parenting while you get out to handle everything else, you might want a mate with Cautious, Energetic, and Social traits.
These wolves will stay behind to keep pack affinity high & take care of pups, but will rely on you for food and territory upkeep.

If you want a mate that can help you take down the best (or the most) prey, you'll probably want Bold, Energetic, and Loner traits.
They'll be more willing to take on more dangerous prey, even if they're not in tip-top shape themselves. They'll keep up the fight when you need to slow down for a moment, and they're less likely to give up the carcass to a competitor; meaning you'll have more food in your stockpile if you can fend everything off.
This particular set of traits is also great if you want a mate that can help with a conquest for LOTS of territory.

If you want the best possible mate for an Ironwolf playthrough, I've found (personally at least) that a mate with Loner, Cautious, and Energetic traits works best, same as the first point.
They're less likely to die, more likely to help with territory & food while you're resting/sleeping, and are very alert when there are predators nearby!
Although, as I said, which mate you prefer is up to you and there's not really a wrong way to go about it, as long as you enjoy yourself.

There are no rules to picking mates!

Please let me know if there's additional info I should add here!