The letter ф is found almost exclusively in loanwords. The only exceptions are sparse native Russian words like дрофа, филин and onomatopoeic words like фу, фыркать etc.
The sound [f], though, can be found in many native Russian words as a devoiced allophone of /в/ in words like вторник, вперёд etc.
It got there after the fall of the reduced, when consonant clusters with /в/ preceding a voiceless consonant became possible. Russian, unlike other East Slavic languages, has readily accepted this sound. Belarusian and Ukrainian instead tend to labialize the /в/ or use prosthetic vowels in the words with etymological weak reduced vowels after /в/
Before the orthographic reform of 1918, there were two letters for the sound [f]: ф and ѳ. The latter was used almost exclusively in Greek and Hebrew loanwords, paralleling the original spelling of these words. It was used, among other words, in the name Ѳёдоръ < Θεόδωρος that you're mentioning in your question.
The two letters denoted the same sound, and the difference between them had never been phonetic, so the latter had been eliminated during the reform.