There is a way to do it if it's really important to you. You see, when the switch starship feature was first introduced, it would list ships by date commissioned. They changed that to alphabetical order later but for a split microsecond, it still loads by date commissioned before it's sorted alphabetically. So if you need this information, you would have to record the screen and freeze frame right after you hit that switch starship button.
Im not sure why its important, but i think the registry numbers go up for every ship commissioned in game, so as long as you didnt change the numbers they should go up in sequence form the earliest to latest ship commissioned in your roster. I could be wrong, maybe another player will chime in and confirm or deny this.
I don't think it'll be worth it to go thru the journal from the beginning of the game. I had assigned registry numbers to each ship as I commissioned them. I recently had the idea to give each of my toons their own (for the most part) registry number and increment the letter for each ship. I had somewhat been doing this all along, but wanted to put the OCD beast to sleep and do it absolutely in order. No biggee, Thank you for your answers.
While a character is part of a fleet each new ship they add to their roster will also add an entry in the Activity Log for the fleet (look under the News option on the home page for the Fleet dialog) with a Stardate and an Entry that reads:
[Character Name] has been given command of the [Ship Name]
I miss when our Captain's logs and starship commissioning were shareable with other player's via the STO website. Using an STO style interface. We had a player Captain search feature. We all play the same missions. But some of those logs were creative writings and enjoyable.
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Answers
I'm not sure what you'd have to search for, though.
[Character Name] has been given command of the [Ship Name]
Hope that helps