R. Schneur Zalman of Liadi (in Tanya, Shaar Hayichud Vehaemunah ch. 4) explains that the name Elokim "shields" the name Havayah, and makes it possible for finite and (seemingly) independent creatures to exist in the first place. Thus, Elokim represents (and is the source of) the tzimtzum, the "contraction" of Divine energy that made "room" for the various spiritual worlds and our physical one.
In ch. 5 he then goes on to relate this to the Midrash that you quoted. An excerpt from the commentary there:
In order for created beings to believe that they possess independent existence there must be the process of tzimtzum, which is an expression of the stern attribute of Gevurah. Without it, all of creation would be completely nullified within its source.
G‑d, however, desired that created beings maintain that they possess independent existence, in order for them to be able to serve Him and ultimately be rewarded for their service. Thus, it is specifically Gevurah and tzimtzum that enable them to realize the ultimate purpose of creation.
So basically, that state of affairs still exists: our world fundamentally gets its energy through the Name Elokim. The "joining" of the Name Havayah to this, R. Schneur Zalman goes on to say, is the fact that our world is capable of being the stage for G-d's miracles. (This distinction between Elokim and Havayah seems to reflect the distinction drawn by Abarbanel, in jake's answer.)