To add a ship profile to the list of your bookmarked ships, select the bookmark icon on the ship profile's header or ship card as shown on the screenshot below. Once added, the icon will turn to color. To remove the ship profile from the list of your ships you can select the bookmark icon again in the same way as when the ship was added.
Bookmark icon on ship card or ship profile overview and the ship profile will show up when ship profiles are filtered based on Bookmarked as shown below.
The bookmark icon is also used in various locations in the Reports section for easier reference and to indicate which ship are marked as your ships.