Stoneless rings are common in other countries. Tattoos are up and coming. A bit more painful, but still cheaper than a diamond (and much more permanent).
Name or initial is not quite the same thing, I think. I don't know anyone who has names or initials as a wedding/engagement tattoo. It's usually a simple symbol, like a rune, or in my case, a Moebius ring (two sides that are one, what better wedding symbolism is there?). Although I do know one person with both a wedding and an engagement tattoo who is about to get a divorce after more than 10 years of marriage.