Double Bass does not imply a Single Bass instrument:
but I was under the impression that the cello was a "tenor"
instrument, rather than a "bass" one.
Perhaps the cello is a tenor instrument in terms of the entire range of instruments, but until the double bass was invented, it was the bass voice relative to the rest of the violin family.
During the Baroque and Classical eras, in quartets and orchestras the cello traditionally played "bass" parts, until Beethoven made a mission of "liberating the cello", by writing more lyrical music for the cello for virtuoso players he knew personally - music that exploited its higher registers.
Still, the origin of the name Double Bass does not seem clear. Here are some ideas:
New World Encyclopedia - Double bass
The instrument's standard English name, double bass, may be derived
from the fact that it is approximately twice as large as the cello, or
because the double bass was originally used to double the cello part
an octave lower.
It has also been suggested that the name derives from its viol family
heritage, in that it is tuned lower than the standard bass viola da
gamba. The name also refers to the fact that the sounding pitch of the
double bass is an octave below the bass clef. The name contrabass
comes from the instrument's Italian name, contrabbasso.
"the sounding pitch of the double bass is an octave below the bass clef" is the best reason offered for calling it the double bass: Its voice is in the 'bass-bass clef' range, although we use the 'single bass' clef to notate its music.