Rian Hughes is known as one of the finest logo designers in comic books. Just one of his many Rennaissance Man skills. You can see his work on DC titles, Valiant and Forbidden Planet logos and plenty more.
In 2002, quite without solicitation, he submitted almost 50 ideas for logos to DC Comics.
Here they are…
The two at the bottom appeared tiny, amongst a bunch of other small logos as part of the cover design for specific one-off books, so although they were used they were not "official" DC logos.