The new job icon blocks this certain icon that indicates if a player is in a party.

[Inanegrain]

I do not know what this icon is called
two of the same in case it breaks.

That's about it, it took a while to realize that it was the job icons that prevented this icon from showing up.

The setting that shows an icon that filled a empty spot when not in a party or an instance being job icons next to names.

[Carighan]

Wat? Sorry, the language just doesn't really parse.

[Eremite]

To clarify what they mean, if you go into Character Configuration -> Display Name Settings (left) -> General tab (top), there's a checkbox for "Display class or job icons with nameplate."

It adds the person's job icons next to their name. It's also has options for coloring peoples' names according to their roles (tank/heal/dps/other).

It's super useful for content like Occult Crescent so you can find healers or other ressers to prioritize raising.

At the same time, when you are in Occult Crescent, it's useful to make parties for doing the content - an easy way to do that is to just look around for the people who aren't in a party and invite them. They have a special symbol that indicates that they're solo/unparties.

That icon is hidden if you have the class icons shown, but other icons are *not* hidden and show next to the class icon. The "Looking for Party" icon shows up for example, but most people don't know to right-click their own name tag and use "Turn party seeker on."

There is also no chat command for toggling the display of these class icons so if you want to toggle, you are forced to menu manually, invite people, then turn name plates back on after your party fills.

[Inanegrain]

To clarify what they mean, if you go into Character Configuration -> Display Name Settings (left) -> General tab (top), there's a checkbox for "Display class or job icons with nameplate."

It adds the person's job icons next to their name. It's also has options for coloring peoples' names according to their roles (tank/heal/dps/other).

It's super useful for content like Occult Crescent so you can find healers or other ressers to prioritize raising.

At the same time, when you are in Occult Crescent, it's useful to make parties for doing the content - an easy way to do that is to just look around for the people who aren't in a party and invite them. They have a special symbol that indicates that they're solo/unparties.

That icon is hidden if you have the class icons shown, but other icons are *not* hidden and show next to the class icon. The "Looking for Party" icon shows up for example, but most people don't know to right-click their own name tag and use "Turn party seeker on."

There is also no chat command for toggling the display of these class icons so if you want to toggle, you are forced to menu manually, invite people, then turn name plates back on after your party fills.

Pretty much this, like bozja, it is an icon that always showed up as an indication someone isn't in a party, job icons next to names till someone... used a third party plugin on it on stream, got banned and got added along with buff timers.
I do not know if that third party tool also blocked this, but it's something I didn't expect to block this specific icon in instances such as OC.