Here are my ideas

Flotilla Excidium:

Frigate: Krennic(Director Krennic from rogue one)

Correlian Corvette: Veers(general Veers from empire strikes back)

Action Transport: Genesis
Flotilla 1

Carrier Class 2: Victory(inspires troops and raises morale)

Carrier Class 1: Inquisitor(Named after the armour, and cause panic and fear)

Braha'tok-class Gunship: Dreadnought (intimidating name)

Correlian Gunship: Korriban(or moraband if you want the stupid canon rename also its the sith homeworld),

Flotilla 2
Carrier Class 3: Bane(Darth Bane, Inventor of the rule of 2)

FLOTILLA 1 (defensive focus)
Quasar Fire-class Cruiser Carrier 1 - Gauntlet
Quasar Fire-class Cruiser Carrier 2 - Pauldron
Braha'tok-class Gunship - Stonewall
DP20 Corellian Gunship - Spike

FLOTILLA 2 (offensive focus)
Quasar Fire-class Cruiser Carrier 3 - Hawkbat Eyrie

EXCIDIUM SUB-FLOTILLA (espionage focus)
EF76 Nebulon-B Frigate - Forsaken
CR90 Corellian Corvette - Lucky Lady
Action VI Transport - Ice Rider

FLOTILLA 1 (defensive focus)
Quasar Fire-class Cruiser Carrier 1 - Defiant
-This is a good name for a defensive focused ship. Defiantly protecting a thing.
Quasar Fire-class Cruiser Carrier 2 - Replusor
-This a good name because the ship literally repulses the enemy.
Braha'tok-class Gunship - Challenger
-This is a good name for a unit that challenges an offending fleet.
DP20 Corellian Gunship - Fearless
-You have to be fearless to be in a glass cannon.

FLOTILLA 2 (offensive focus)
Quasar Fire-class Cruiser Carrier 3 - Avenger
-I chose this name because it sounds like a good retribution name.

EXCIDIUM SUB-FLOTILLA (espionage focus)
EF76 Nebulon-B Frigate - Phoenix
-This ship represents a new beginning for the House, and needs to be flexible as it asserts itself in its new role.
CR90 Corellian Corvette - Rogue
-This ship would be off doing its own thing from time to time, so Rogue make sense.
Action VI Transport - Trojan
-This ship plays one role on the surface (transport), but in actuality is a mobile shipyard.

QF1: The swarm. reason: It is a fighter carrier, and TIE units usually use swarm tactics to overwhelm.
QF2: the Watchful mother. Reason: It is also a fighter carrier, keeping an eye on a sector and able to intercept enemy forces.
Braha'tok: the Vigilant Eye. Reason: built to defende larger vessals from enemy fighters.
DP20: the Swift Guardian. Reason: The DP20 is a fast ship, but also has a lot of heavy weaponry
QF3: The Opperessor. Reason: In battle, the fighters will oppress enemy ships
EF76: Emperor's Might. Reason: These ships are quite dangerous, and can punch through enemy lines.
CR90: The Agression. Reason: They can be used for fast and aggresive combat.
VI transport: Big Rig. Reason: lol

FLOTILLA 1:(I have pretty much made both Quasers sister ships.)
Quasar Fire-class Cruiser Carrier 1- Legacy (Legacy representing what the clan has gone through and the legacy it has left behind)
Quasar Fire-class Cruiser Carrier 2- Destiny (Destiny representing what the clan has yet to achieve in the future)
Braha'tok-class Gunship- Protector (seeing as this is a defensive fleet and it is an anti-fighter/screening vessel)
DP20 Corellian Gunship- The Bottle (Cause who i CSP doesn't enjoy drinking)
FLOTILLA 2:
Quasar Fire-class Cruiser Carrier 3- The Dragon (Going back to the design of the Clan symbol)
EXCIDIUM SUB-FLOTILLA:
EF76 Nebulon-B Frigate- Noghri (Named after the skilled and stealthy assassin species called Noghri)
CR90 Corellian Corvette- Nightfall
Action VI Transport- The Inconspicious

FLOTILLA 1 (defensive focus) Quasar Fire-class Cruiser Carrier 1 - Emperor's Hand
Quasar Fire-class Cruiser Carrier 2 - Emperor's Voice
Braha'tok-class Gunship - Ender's Pride
DP20 Corellian Gunship - Golem

FLOTILLA 2 (offensive focus) Quasar Fire-class Cruiser Carrier 3 - Quickstrike

EXCIDIUM SUB-FLOTILLA (espionage focus) EF76 Nebulon-B Frigate - Shadow Strike
CR90 Corellian Corvette - Emperor's Pride
Action VI Transport - Firefly

FLOTILLA 1 (defensive focus)
Quasar Fire-class Cruiser Carrier 1 - Pellaeon
Quasar Fire-class Cruiser Carrier 2 - Fel
Braha'tok-class Gunship - Lecersen
DP20 Corellian Gunship - Piett

FLOTILLA 2 (offensive focus)
Quasar Fire-class Cruiser Carrier 3 - Pestage

EXCIDIUM SUB-FLOTILLA (espionage focus)
EF76 Nebulon-B Frigate - Sloane
CR90 Corellian Corvette - Tagge
Action VI Transport - Yularen

FLOTILLA 1

Quasar Fire-class Cruiser Carrier 1 - PONTIFEX
(Ancient rank of the Krath Order, once conferred on those versed in dark necromancy.)

Quasar Fire-class Cruiser Carrier 2 - CUCHULAIN
(In honor of a former member, Cuchulain was one of CSP's core founders and the first Clan member bestowed with the name of Palpatine. https://wiki.darkjedibrotherhood.com/view/Cuchulain_Darkblade_Palpatine)

Braha'tok-class Gunship - MANTICORE
(A legendary flying predator or yore, with the head of a man, the body of a lion, the wings of a giant bat and the tail of a dragon.)

DP20 Corellian Gunship - HYDRA
(A many-headed serpent of ancient mythology.)

FLOTILLA 2

Quasar Fire-class Cruiser Carrier 3 - THRASHER
(A person or device which beats repeatedly and violently with a stick or whip.)

EXCIDIUM SUB-FLOTILLA

EF76 Nebulon-B Frigate - SUBTERFUGE
(The use of deceit to achieve ones goals.)

CR90 Corellian Corvette - CONSPIRATOR
(One who colludes in subterfuge.)

Action VI Transport - BLACKBIRD
(An avian creature that flies only under the cover of darkness; also, a primitive atmospheric spy craft of antiquity.)

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Rhaub D'ar Aghasett-Palpatine 288

Flotilla 1: Shield Wall
Quasar 1: Shield of Ptolomea
Quasar 2: Bastion of Caina
Braha'tok-class Gunship: Tempest
DP20: Guardian

Flotilla 2: Dagger
Quasar 3: Glory of Judecca

Excidium:
Neb Frigate: Expeditious
CR90: Venture
Action VI: Lady Death's Galley

FLOTILLA 1 (defensive focus) Quasar Fire-class Cruiser Carrier 1 - DRAGON SCALE Quasar Fire-class Cruiser Carrier 2 - ANDROMEDA Braha'tok-class Gunship - ZEALOT DP20 Corellian Gunship - NIGHTBREAKER

FLOTILLA 2 (offensive focus) Quasar Fire-class Cruiser Carrier 3 - UNNECESSARY EVIL

EXCIDIUM SUB-FLOTILLA (espionage focus) EF76 Nebulon-B Frigate - ABYSS STALKER CR90 Corellian Corvette - NIGHTMARE Action VI Transport - SILENT GHOST

FLOTILLA 1 (defensive focus) Quasar Fire-class Cruiser Carrier 1 - Void's Sword Quasar Fire-class Cruiser Carrier 2 - Foul Saber Braha'tok-class Gunship - Mandalore DP20 Corellian Gunship - Dragon's Greed

Named after famous GE Admirals of lesser famousness (idea came from East Berlin naming their minor streets after minor Communist heroes, and heroes of the people, while their major roads were named after major Communists).

FLOTILLA 1 (defensive focus) Quasar Fire-class Cruiser Carrier 1 - Jerjerrod
Quasar Fire-class Cruiser Carrier 2 - Piet
Braha'tok-class Gunship - Tagge
DP20 Corellian Gunship - Tenant

This title is in honor of Dooku, who "sacrificed himself" for the adoption of the Galactic Empire as a system in the Republic.

FLOTILLA 2 (offensive focus) Quasar Fire-class Cruiser Carrier 3 - Tyranite

Since HEX might become a Security Corporation of sorts, maybe easy sounding official security names would be better.

EXCIDIUM SUB-FLOTILLA (espionage focus) EF76 Nebulon-B Frigate - Vixus One
CR90 Corellian Corvette - Vixus Two
Action VI Transport - Vixus Three