Marriage is definitely a thing, though you are right that there isn't actually any definite evidence that Gascoigne and Viola, or any commoners for that matter, actually engage in marriage.
[QUOTE=Ring of Betrothal]The inhuman beings known as the Great Ones imbued this Ring of Betrothal with some special meaning. 

In the age of the Great Ones, wedlock was a blood contract, only permitted to those slated to bear a special child.[/QUOTE]
This suggests that marriage is considered even more sacred in Bloodborne than it is on Earth; something, at least at one time, only allowed for a select few. Given that the ring specifies "in the age of the Great Ones" and that you can use the ring to propose to Queen Annalise, however, it seems likely that marriage has become a more widespread practice since those days. (The bit about Queen Annalise would, ironically, not be evidence on its own, given that she has her Hunters collect "blood dregs" (cough) so that she can bear a "Child of Blood" to succeed her, which certainly [i]sounds[/i] like she is a person "slated to bear a special child".)