This is from memory, so may skip ships I don't regularly use or are stored somewhere I haven't been for a while:
Corvette - Wayward Wanderer. Combat focused multi-role, legacy engineered. I got bored around October 2016 & took this 19ly ship on an 18 month grand tour of the galaxy. Reached Beagle Point in July 2017, spent the new year '17/'18 in Colonia & returned to the bubble in March 2018. Still gets brought out occasionally for assassinations & was regularly used for CZ duties before the 3.3 changes. My favourite ship.
Corvette - Number Two (named for the 3.3 exploration & swear filter changes). An attempt to improve on my first Corvette with new post 3.0 engineering, has a 30ly jump range with a guardian FSD booster. Used for armed exploration.
Cutter - The Golden Goose (ie don't kill me

) multi-role trader with 512t capacity, C8 Bi-weave shield with three shield boosters, it has around 2,000 shields & 2,200-ish hull armour, used for Open large pad mission running & currently station repair A-B trading.
Cutter - Bait. Shieldless 792t trade cutter bought specifically for repairing stations. The slightest scratch costs thousands & I enjoy the challenge of flying shieldless (usually in solo). Has a combo of rail guns & frag cannons to give any attacker a bloody nose but it's not designed to kill anything.
Conda - Legs Eleven. 75ly exploration paper aeroplane, equipped for self sufficiency & a single small beam for 'experimenting' with whatever I find.
Conda - Pax Lap (a reference to IRL track days). Bought specifically for rescuing refugees from burning stations.
Python - Transaction. Medium pad BGS mission runner & daily driver in the bubble, 200t capacity with C6 Bi-weave shields.
Python - Thug. This was the ship that got me to combat Elite in 2015, it has always been a dedicated CZ ship & is my only ship with no cargo space, it's filled with defensive modules to stay in the fight. Main weapon is a long range C3 fixed beam (most of my ships have at least one fixed beam).
T-9 - "Maggie" (this iron lady's not for turning (no political affiliation)). 736t of open viable cargo hauling for maximum Open play trade capacity. Small shields & reinforced internals, designed to survive piracy.
T-9 - Cattle Grid. Originally bought to transport refugees before realising the Conda could carry more, now converted to a 784t shieldless (but armoured) trader. Only used in high security systems & generally gets shipped around to wherever I need it because it's cheap & I don't mind losing the occasional hull in the name of entertainment (trading can be dull

)
Krait MkII - Tony (ie the tiger, it's Krait!!). Ostensibly a replacement for Thug the CZ Python, gets taken out when I fancy a change but I prefer the more challenging flight characteristics of the Python.
I own several
Cobra MkIIIs, mostly the same loadout & stored in strategic locations for taxis/light BGS work & exploration. Lightly armed & armoured, super fast & fun to chuck about. '
Gunrunner', '
Frenetic' & '
The Original' (the earliest hull I still own) are the ones I remember the name of.
Cobra MkIV - Minor (pre-3.3 mining ship). Used for getting the Bromelite to unlock an engineer, I hate mining so it seemed fitting that the CIV would be good at it.
Cobra MkIV - Protractor. Exploration build, used once & left somewhere in frustration, I shipped a taxi over & flew the taxi home. I'd remote sell it if I wasn't such a miser.
Sidewinder - Zip. Exploration build with enhanced drives. Used for scouting CG & other high player traffic systems and exploring in the bubble.
Sidewinder - Velcro. Combat build, only really gets used for occasional wake scanning sessions now.
I have other ships but these are the ones I use regularly & have named (and can remember without checking

)