The reason this letter writes f is a piece of Greek history that Slavonic inherited without being party to it.
In classical Greek the letter theta wrote an aspirated t, a t followed by a puff of breath, distinct from both the plain t and from any fricative. Over the following centuries that sound changed, as the corresponding sounds in the same series did, into a fricative made with the tongue against the teeth, the sound English still writes with th.
Slavonic had no such sound. Faced with a Greek fricative their language did not contain, Slavs substituted, and the substitution that prevailed was f. Some words show t instead, and the doublets that result are still visible in Russian personal names, where the same Greek name appears in two forms, one with f and one with t, according to which route it took.
Three things follow. The letter name fita records the substituted sound rather than the Greek one, so the name itself is evidence for the pronunciation Slavs actually used. The pairing with fert is not a redundancy in Greek terms, since phi and theta were entirely different letters, and only becomes redundant once both are being read as f. And a Slavonic spelling can therefore tell a reader something about a Greek word that the Slavonic pronunciation conceals.
The letter is a small piece of evidence for the state of Greek in the ninth century, preserved by a language that had no use for the distinction it records.