We all maintain that each Vedic hymn is associated with a devata, Chanda, and rishi as maintained in Anukraminika. But what is the source of our that belief? Where it has been written that verse has to be associated with a devata, Chanda & rishi? Is there specific verse from scripture that's revealing the fact?
Each mantra was revealed by a specific rishi, composed in a particular poetic meter and dedicated to one or more deities. As the Veda is a collection of mantras passed down from the time of the rishis, these attributes (devatA, RShi, chandas) have been an inseparable part of each mantra.
यत्काम ऋषिर्यस्यां देवतायामार्थपत्यमिच्छन्स्तुतिं प्रयुङ्क्ते तद् दैवतः स मन्त्रो भवति
The mantra belongs to the deity who is eulogized by the rishi with a specific desire that the deity can fulfill.
For the deity, the formula given in Nirukta 7:4 is provided.
“The stanzas whose deity is not specified, such stanzas belong to the same deity to whom that particular sacrifice, or a part of the sacrifice, is offered. Now, elsewhere than the sacrifice, they belong to Prajapati according to the ritualists; and to Narasamsa according to the etymologists.”