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I do not know how reliable http://cleo.lcs.psu.edu/boy_names.html is, but they have all external indications of being trustworthy. Note also that there may be an old English farnham, which in many pronounciations would sound very similar.
According to the site farnam is the masculine version, and farinam is the feminine one. Both of them are given the meaning `glorious+name'. Both the grammatical structure and the meaning sound familiar, though I know next to no Farsi.