To display forum rank you need to create a new fieldtype of "Forum Status" then within Parameters > Display set "Status" to "Rank". The rank it outputs is entirely coming from Kunena API. So if it shows moderator then that's just what Kunenas API is responding with, but it typically happens when the user is a moderator of at least 1 forum category.

Looks like the Kunena rank API can be sent a category id to filter it down to only checking moderator status of a specific category. That doesn't really make sense in the context of a CB field though as the CB field is to output their global forum rank. Since your user is a moderator of at least 1 category it outputs them as moderator.

It looks like I can add a new substitution like karmaplus and karmaminus to output the rank provided by Kunena it self. Have added a feature ticket for this.

forge.joomlapolis.com/issues/5673

Once the MR has been merged we'll release a new nightly and you'll be able to use all of the following in the sidebar parameters.

[karmaplus]
[karmaminus]
[karmatitle]
[karma]
[rankimage]
[ranktitle]
[posts]
[thankyou]
[points]
[medals]
[personaltext]

Those are all that Kunena provides. Specifically [rankimage] and [ranktitle] will fit your needs.

We use peer review for all our merges and Beat is busy at this time so it maybe until Monday before it's merged.