beside trademark as usual?
As far as I am aware, electrum is not a company, so it requires no trademarks.
I believe that as it is open source, the logo and any related content unless explicitly stated otherwise where they appear are completely free from copyright and are released under the MIT licenses meaning they are copywritten but are avaliable for you to copy, edit or redistribute anything that they make in relation to electrum (providing it does not break any laws or the object in the program is explicitly protected by copyright).
It's a great gift to us from the developers that none of it is really restricted by copyright and it's probably a nice gesture to mention where you get the logo from.