In the old DarkBasic.com FAQ (not there anymore) it said that the Dark part of the name was not an evil conatation, rather that this product is a "Dark Horse" in the fact that it is deceptively easy to use, but is capable of impressive results. So the DARK part doesn't stand for anything specific.
B.A.S.I.C. however, stands for Beginner's All-Purpose Symbolic Instruction Code - a system developed at Dartmouth College in 1964 under the directory of J. Kemeny and T. Kurtz. It was meant to be a very simple language to learn and also one that would be easy to translate. Furthermore, the designers wished it to be a stepping-stone for students to learn on of the more powerful languages such as FORTRAN or ALGOL.
DarkBasic uses the structure of the early versions of BASIC, adds direct x support and new commands to make it suitable for 3d applications.
Hope this helps and welcome back