Slitherine

I'm confused between the option to delete or permanently delete a ship design. I'm afraid that if choose the permanently delete option, I'll delete that ship design such that it won't appear when I start a new game. Is that true? Also, when I delete a ship design, I want to carry over the name to the upgraded ship plan but it won't let me do that instead it puts a number on it.

Yes, permanently deleted designs wont appear in the next game.
You need to permanently delete or rename the existing design to free the name. Renaming seem to be less destructive.