ekeyoudaoicibaDictYouDict[eke 词源字典]
eke: [12] No Old English evidence of this verb, which originally meant ‘increase’, has been found, but related forms in other Germanic languages, such as Old Norse auka and Gothic aukan, suggest that it did exist. Both these and a range of non-Germanic verbs, such as Latin augēre (source of English auction, augment, and author) and Greek aúkhein, point to an ultimate Indo-European ancestor *aug- (from which comes English wax ‘grow’).

The first syllable of nickname was originally eke. Until comparatively recently English had another word eke [OE], which meant ‘also’ (German auch and Dutch ook ‘also’ are related to it). It is not clear whether it is ultimately the same word as the verb eke.
=> auction, augment, author, nickname, wax[eke etymology, eke origin, 英语词源]
eke (v.)youdaoicibaDictYouDict
c. 1200, eken "to increase, lengthen," north England and East Midlands variant of echen from Old English ecan, eacan, eacian "to increase," probably from eaca "an increase," from Proto-Germanic *aukan (cognates: Old Norse auka, Danish öge, Old Frisian aka, Old Saxon okian, Old High German ouhhon, Gothic aukan), from PIE *aug- (1) "to increase" (see augment). Now mainly in phrase to eke out (1590s), wherein it means "to make a supply of something go further or last longer." Related: Eked; eking.
eke (adv.)youdaoicibaDictYouDict
"also" (obsolete), from Old English eac, cognate with Old Saxon, Old Dutch ok, Old Norse and Gothic auk, Old Frisian ak, Old High German ouh, German auch "also;" probably related to eke (v.).