Notes:
• I wasn't sure about their size, but in the end I decided that the scale on my A4 paper if going to be 1cm = 1km so the top ship is 27,5km long while to bottom one is 19,5km long.
• When making this, I tried to focus on the aestics, so when it comes to the lenght of the generation ship from the Migration timeline: I would make it at least the double of its current lenght to add more fuel tanks and larger propulsion and radiators. Currently the fuel tanks are size-wise on the edge of giving the ship enough velocity so the bussard ramjet is at operational speed. And not let me started on the instanity when it comes to planning gravitational slighshots and other maneuvers to slow-down in the destination solar system with the small amount of fuel the ship could carry this concept (you cannot really use the collector when it is not facing prograte after all).

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The Migration timeline
Despire the use of biotech, anthin ships are closer to the near-future human interstaller vessels. Despire not every ship being exact like the others in the migration fleet, they all lack on-ship FTL and ability to generate artificial gravity - thus these interstaller vessels simulate gravity by constant acceleration/deceleration or by centrifugal force when on orbit and are limited to sub-light speeds.
Due to The Great BirthGiver's moon being [dissasembled] Anthins would lack easy access to Helium-3 like we humans have on our Luna's regolith and would need to first contruct solar wing collection structures if they would want to use fusion rocket engines. For this reason, the engines, that give the starting push to make the collector of the bussard ramjet operational, would use nuclear fission.
Aside using swarm tactic where other ships can assist if one ship experiences mission-enderaing accident or fatal malfunction instead of sending single vessel, the anthin generation ship would have multiple major components instead of few. Best example being the engines: in case of some malfunctioning and becoming unrepairable, the vessel is able to sustain thrust symmetry at the cost of maximal thrust.

The Conquest timeline
Much smaller but with more features. With InderDimensional Patrol's technology anthins stole aquired in this timeline, the ships pack equipment that no longer make interstallar voyages something to transoceanic crossing on wooden sail ships but to transoceanic travel on modern jet airplace.
Aside gravity generators, inertial dampeners, shield generators and hyperdrive with trasuniversal jumper, the most notable technology of these spaceships is a small artificial transdimensional wormhole which is connected to young universes which space is like thick soup of particles like helium and hydrogen, essencially giving the ships infinite fuel for reactors and thrusters as long the wormhole is kept opened.
As it is written on the concept image itself: invidual royal ship is modified to the queen's need as it not only serves as command center for the section of the swarm she is responsible for but also her mobile residence. The royal ship on the concept art is shaped with focus on combat in mind which is it has design aspects like radiators resembling dorsal fin of Perch fish, however, royal ship belonging to queens that focus on other aspects like reseach or diplomacy would have vessels with structure language communicating assignment - I for example imagine that Berta's royal ship for example would have radiators shaped like the ones one the concept for the generation ship.
I do not plan to give any rules for the names for Anthin vessels as Anthins themselves aren't culture that gave any value to names for inviduals before the arrival of offworlders like Kotjeslav. However, the name for one of these royal ships I'm 100% sure about is for Helena's: "Dragon"