Well, as Ed said, it depends greatly on what time period (and even what decade), as well as what region. It also depends on what class of person.
Yes, people did get fully custom weapons for themselves, but they also bought them "off the rack", or where issued a standard weapon, and all of these things go on throughout most of the medieval, renaissance, and pre-modern eras of the Western world. The one thing that did not happen was the idea of one bladesmith making weapons himself. It almost always was done where one guild made the blades, one made the hilt fittings, etc.