I just made a restart GaCorpSolar and it gave me Solar Engineering id but under the name of Commonwealth of Liberty.
so after checking the owned bases by Commonwealth of Liberty I found that they have 2 bases, Planet Guadalajara and Alexandria Base.
after reading the infocard of Planet Guadalajara it says:
The planet Guadalajara is the sole habitable world of the Vespucci system, home of the Commonwealth of House Liberty, a separatist government formed by the Hellfire Legion in 822 A.S.
so if I understand well. this means that Commonwealth of Liberty is not Solar Engineering.
maybe a developer need to check this and fix/separate both ids.