If the ship is just damged and not destroyed, you cannot claim it. If it is already destroyed and shows up as Wreck, you might be able to "Tag" the wreck to claim it as your own, but I'm not sure about the specifics.
Only recycling factions own the necessary equipment/facilities and can salvage wrecks. And I would be surprised if "your" wreck hasn't already been claimed by one (if it's not owned by someone else). If you scan it, who is shown as owner?