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.
My best friend is a tattoo artist. He said the top two coverups he does are for:
a. band names
b. significant other initials or names
He joked that its practically a harbinger of a failed relationship since most are back in his chair within 12-18 months to get them covered up.