In 'A Fire Upon the Deep', the alien species that communicates through shared consciousness is the Tines.
Created by science-fiction author Vernor Vinge, the Tines are dog-like beings whose intelligence is distributed across small groups called packs. An individual Tine is not equivalent to a complete human mind; the pack functions as the conscious person, with its members communicating through short-range ultrasonic signals produced by specialized organs called tympana.
This makes the Tines an unusual form of group mind. A pack can think, speak, remember, and develop a personality, but its identity changes when members are added, removed, or killed. The novel uses that biology to explore questions about individuality, identity, politics, loyalty, and the meaning of personhood.
The Tines inhabit a planet in the Slow Zone and have a civilization roughly comparable to the human Middle Ages. Important groups include the Flenserist faction and Woodcarver's pack, whose conflicts drive much of the novel's planetary storyline. The other options are not the species described: the Blight is a superintelligence, Straumli Realm is a human civilization, and 'Riders' is not the canonical answer.