Is there any opposite name for Decibel?
Most of the time, it's the ratio of a physical quantity to a reference. The reference can either be an industry standard (Example: dBSPL, dBm, dBu etc.) or some other suitable quantity (Example: voltage at the input of a filter). 

"Physical quantities" in audio are things like pressure, volume velocity, particle velocity, displacement, voltage, current, force, etc. (20 log) or sometimes also power, energy, or intensity (10 log).

For example: a microphone measure "sound pressure" as a physical quantity and to make it logarithmic you use

$$P = 20 \cdot log_{10} (p/p_0)$$

where $p$ is the original sound pressure, $p_0$ a suitable reference pressure, (20 micro Pascals is industry standard) and P the resulting sound pressure level in dBSPL.

Taking a ratio is very important, since it also takes care of the units. In digital signal processing, you often just deal with numbers (without units), but a proper choice of reference is still important. Typically choices are either digital full scale, some suitably calibrated physical quantity or just simply "1" . The reference is important: a dB value without a well defined reference (implicit or explicit) is meaningless.