You an use items recovered from wrecks in your own ships.  There are a couple of things you will need to do however.  The first part is in the ship design screen (F5) design view tab. There is a check box below the component list for using only your own tech.  You will need to uncheck that so you can see any components that you have salvaged.  You then need to make a new design of ship to use the components.  Even if you later have the exact same components designed yourself they will not be compatible between ships, you will have to have two different designs, and build them separately.  I usually design a class that I can build then replace what can with the salvaged parts so that the same shipyard can usually build either design. 

You can do the exact same thing with parts recovered from ruins, or if an empire will trade with you and give or sell parts to you.  (currently only a player run race will do this however)

Brian