Here is my tested theory:

In my server I often change the faction players start out with. There's a bunch of lines in the mpnewchracter.fl file that set what each faction feels towards you. There's also an empathy.ini file that describes how each faction feels towards every other faction. When I applied the default factions to a new character, the tag shows up properly. Outcast, Blood Dragon, Navy, Rheinland police, Bretonia police, and many others show up beside my name just fine.

Do you want to have the zoner tag next to your name? You need to be as close to neutral with all factions as possible. For factions like police or criminals, you need to like, hate, and be neutral to the same people as they do. The close you come to the faction settings in the empathy.ini file, the more likely you'll get their tag on your name. It has nothing ot do with your ship, your creds or weapons, and not just how the faction in question feels about you, but how all factions feel towards you. Hope this clears things up.

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There is no knowledge that is not power.

Sorry to bring up an oldish thread, but I may have some information on the rep tag issue.

It has been mentioned before that by editing mpnewcharacter.fl values you can start off with whatever faction tag you want. In my experience, this does not mean matching the empathy values with the faction you wish to join, instead all that was required was setting the faction you wanted in front of your name to anything above +0.901 on the reputation scale. The cutoff limit between ther usual "max green friendly" we usually see in MP and the "yellow flashing" max green friendly seems to be a reputation value between +0.9 and +0.901. If there was a way to remove the limit in MP which restricts your rep to below +0.901, then I assume you would gain an affiliation to a faction, and be able to lose that affilliation and join other factions you are also friendlier than +0.9.

The evidence of this comes from an example given where you start MP with a new character, select and abort 5 missions from Navy during the launch, and a message on the hud will say "Lost affiliation: Liberty Navy New affiliation: Liberty Security Force". This occurs because in vanilla Fl, the mpnewcharacter.fl file has navy and LSF both at +0.91 reputation. By aborting the 5 or so navy missions, your rep with them declines until about +0.64, while your LSF rep is still 0.91 - the game then switches your tag to LSF and announces this to you.

The point of this post is that if someone could find where the game limits your max rep with factions to below +0.901, and increase that limit to say 0.91, the tag system in MP may work as it was intended.