Note:
(a) Maxime. Think Baby Names, undated www.thinkbabynames.com/meaning/1/Maxime
(i) Its nickname is maxie, for both male and female.
(ii) The male given names Maximo (Italian) and Máximo (Spanish), together with Maxime, are all derived from Latin adjective Maximus:
" (superlative of magnus [(adjective masculine; neuter form: magnum): 'large, big, great']) greatest, largest, most powerful
en.wiktionary.org/wiki/maximus
(b)
(i) The first monarch who adopted the name Maximilian was Maximilian I, Holy Roman Emperor
en.wikipedia.org/wiki/Maximilian_I,_Holy_Roman_Emperor
(1459 – 1519; Holy Roman Emperor 1508-1519; His father, Frederick III--Holy Roman Emperor and Eleanor of Portugal--named him for an obscure saint whom Frederick believed had once warned him of imminent peril in a dream)
(ii) Maximilian
en.wiktionary.org/wiki/Maximilian
(a male given name in German; Etymology: Saint's name from Latin Maximilianus, a derivative of Maximus "the greatest." It was used in German royal houses after Friedrich III chose it for his son in 1459, explaining it as a combination of the names of two Roman generals, Maximus and Aemilianus)