'uniheaded' originates from Latin-derived prefix 'uni-' (from Latin 'unus' meaning 'one') combined with English 'head' (from Old English 'heafod'), where 'uni-' meant 'one' and 'head' meant 'the upper part or leader'.

'uni-' entered English via Latin/Old French influence and combined productively with English nouns and adjectives in Modern English; 'head' comes from Old English 'heafod' and remained as 'head' in Middle and Modern English, producing the compound 'uniheaded' in modern coinage by analogy with similar compounds (e.g., 'single-headed').

Initially, the components meant 'one' and 'head' respectively; over time the compound came to mean specifically 'having one head' and by extension 'led by a single head' in figurative use.