I believe his parent's (or potentially legally designated guardian's) choice to assign him the title of 'Big Hat' at birth can be attributed to naming traditions that rose to prominence in the United Kingdom during the English renaissance. Said custom entailed that the choice of a baby’s surname was to be made with the intention of ensuring the child grows up to inherit the traits said surname promises- ex: Giving a child the last name 'Smith' with the hopes of them growing up to be a blacksmith. While this practice is long since archaic, its legacy has survived to the modern day, as occupation based names such as Smith, Miller, Hunter, Baker, Mason, and Carter dominate the Western world today. It’s important to note that while the aforementioned naming convention likely originated around the joint Anglo-Saxon occupation of mainland Britain, (which, to put into perspective, directly followed the fall of the Roman Empire) it didn’t become a cultural staple in the region until many centuries later, when a surge in commerce and culture allowed the return of artisan crafts. In reality, the presence of the manor-centric class structure that dominated the European Middle Ages (colloquially known by historians as 'The Dark Ages' or 'The Middle Ages') while at the time necessary for maintaining a form of social order, ended up rendering the centuries during which it occupied western Europe in complete cultural limbo. The name ‘Logan’ itself derives from an ancient Gaelic (Scottish) dialect, and with Scotland notably being a major geographic part of Britain, we can conclude that, at least in part, the character has direct heritage in the Great British region. Now when considering the name “Big Hat Logan” ’s etymology and the historical context of the unorthodox title, we can conclude that indeed, Logan’s parents named him as such because they aspired for him to wear a big hat.