I realize that it was once more accurately called Dahomey, but why the name change?
Two major reasons:
Geography. Benin is located on the Bight of Benin, which took its name from the very empire that you mention.
A political statement. The name Dahomey was French, and after independence, many wanted to distance themselves from the colonial identity. Benin was an acceptable choice because it drew a distinct parallel from the newly-established state to a fairly powerful African Empire that existed prior to colonial intervention. In addition, Dahomey only covered the central portion of the modern state. The name Benin was more inclusive of the other regions integrated into modern Benin. The other official name changes (from the People's Republic of Benin in 1975 to the Republic of Benin in 1990) reflect the change in the political structure of the country, moving from Marxist-socialism to a kind-of democratic-republic.
There may be more, but this is what I remember from a few lectures by Bonnie Smith at Rutgers. Africa certainly isn't my specialty, but these types of naming conventions follow some broad patterns across societies.
The answer is more geographical than historical: the name comes from the Bight of Benin, a curve in the coastline which includes Benin. Dahomey on the other hand was a kingdom which only reached across what is now the country of Benin. To call it Dahomey would be to not represent the whole country, favoring the coastline. To call it Benin seems arbitrary, geographical, and therefore neutral.
Sorry for the lack of citations, but this is all easily confirmed just through looking at names, I'm not sure what I would use as a source!