'single-headedness' is formed in Modern English from the adjective 'single' + the adjective 'headed' (from 'head' + past-participle suffix '-ed') and the nominalizing suffix '-ness'.

'single' ultimately comes from Latin 'singulus' via Old French/Middle English (yielding Middle English 'singel'/'single'), 'head' traces to Old English 'heafod' which became Middle English 'hed'/'head', and the suffix '-ness' comes from Old English '-nes(s)e'. These parts combined in later English to form the compound adjective 'single-headed' and then the noun 'single-headedness'.

Initially the component elements simply meant 'one' (from 'single') and 'head' (from 'head'); over time they were compounded and nominalized to mean the abstract state of 'having one head or one leader' as used today.