Etyomologically speaking, the word “Ranger” means “a (mounted) man who polices an area”. This is taken from the Germanic word “rengen”, or Old French “rengier”, circa 13th century, which means “to move over a large area, to roam with the purpose of searching or hunting”
And so, while the term does have connotations with regards to being close to nature as scouts and guides (e.g. US Army Rangers that worked with Native American tribes during the American colonial period), there’s really no direct relationship to the word “range” as in the upper and lower limits of a certain distance.
Even if we were to look at D&D for inspiration, it’s important to note that at no point is a D&D Ranger obliged to use a ranged weapon – their trademark is the ability to have Favored Enemies, have an Animal Companion, be able to Track targets and move swiftly and silently through woodland areas. If anything, having to choose between Archery and Two-Weapon Fighting as the D&D Ranger’s preferred combat style allows a player to repudiate bows altogether as an deliberate choice.