Well, it would depend on how formalised your security is. If security is contracted to a PMC, then they might have a more militarised structure. Otherwise, it's likely to be quite simplified with fewer hierarchical tiers, being arranged by location rather than by specialties.
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I'd argue that pro-actively shooting pirates is very much your job if it's in the interests of your corporation and results in enhanced profit in the long term.
In IMG, we just have Recruit (across all characters, Paramilitary or otherwise), then Defence Force Pilot as part of the Guild Paramilitary. Occasionally the Guildmasters make an appearance on the battlefield, and you have those with the Mark of the Vanguard who technically are heroes of the Guild or something.
You can make it as simple or complicated, and as militaristic as you feel like. Perhaps "Pebble-grinder", "Rock-cruncher" and "Rot-crusher"