Seriously? Any historical accounts of people choosing this out? Do their descendants still bear that name? I find it amusing that people walking around Israel in 2005 might be called No-Sandals because a distant ancestor refused to marry his brother’s widow.
Nearly all modern Rabbis (going back a long, long long time) have regarded levirate marriage as icky. The sandal ritual is virtually mandatory, nowadays, so no fuss is made about it.
But they’re still doing it? And those guys are still called No-Sandals?
Seriously. I’m nearly always serious, except when winding up Americans about quaint British customs. This was a quaint Biblical custom, and doesn’t qualify.
…Although I’m delighted to learn that it persists in some form, even when levirate marriage is no longer practised. 
Pro-forma, yes, it’s still done, because the Torah says you have to. But since it’s no longer regarded as in any sense a dishonor, the “name” bit is forgotten.