First some context. Western music began with monophonic Gregorian chant. The most common note sung was the 5th degree, which led to it being named the 'dominant'.
Western music derived it's modal system from the Greeks and others, using a division of the octave into 7 distinct notes using only whole and half steps. Renaissance composers routinely sharped leading tones at cadences and lowered the fourth in the Lydian mode, and effectively only the Aeolian and Ionian modes were in general use by the Baroque, and became known as the natural minor and major scales, respectively.
In the early 1700's, Rameau published "A Treatise on Harmony" in which the modern chord classification was documented, including the building of chords in 3rds and using the highest chord note above the 5th as part of the chord name. This classification was done based on the major and natural minor scales.
Since traditional theory is based on the major scale, and the only degree in that scale that a major chord with a flatted 7th occurs naturally is on the 5th degree (dominant), the chord structure is called a Dominant 7th.
Dominant 7ths can be played on other degrees, and are often called 'secondary dominants', but they have one or more notes in the key altered in order to get the root, major 3rd, perfect 5th, minor 7th structure.
The answer is that the name 'Dominant 7th' is given because the structure of a dominant 7th only naturally occurs on the 5th degree.