I don't see any names (printed with the STOP font) on the warships. If you want more eyecandy you can add them (tuto: Idk where to find them, I am sure they are on the forums somewhere. I could look but its kinda late here).
Also in the first screen with the GTxC. Isn't the capship a bit too close to the star? In WiH at the last mission the Indus was pretty much at the same range from the Sun and half [80% to be exact] their crews were dying from radiation poisoning .
Dohohohooo obligatory BP derail :p
The Indus was a lot closer to the sun than that ship is, and BP physics don't necessarily apply to the rest of FS. If a ship has the armor to protect the crew from direct hits from multi-gigaton nuclear weapons, it can probably hang around near stars.