Sorry, but is a very big deal. Taking the husband's surname as her own, cements the familial bond, and announces to the community that 'these people are now a unified family unit'.
If the woman has "various reasons" for keeping her maiden name that are more important than her marriage, then that just shows you where her priorities lie. I mean, what's the point of getting married, if you're going to retain your singular identity? May as well just shack up. You haven't really committed, in my view.
My Gf and I are "shacking up" as you call it. We were literally best friends, inseperable as a matter of fact, for a long time before becoming romantictly involved. We literally do everything together and have all the same interest in life(working out, running, cooking etc). I know for fact we have a stronger, more loving relationship than many married folks and many married people have told us that.
I know several couples who have never been married, produced several kids and have been together faithfully for 30+ years.