I checked the numbers. OpenOffice reports about 230,000 downloads a week. LibreOffice, in contrast, reports about 1,000,000 downloads a week. Those are both direct downloads from their respective websites, thus not counting Linux distributions, in which the default office suite is LibreOffice. AFAIK, no distribution comes with OpenOffice as its default; it's always LibreOffice.

I also checked Google Trends for the last 3 months, comparing LibreOffice vs OpenOffice. The first is searched on average 4.7 times more than the latter, which tracks with weekly download numbers.

From those numbers, I'd say it's pretty clear the name "LibreOffice" won quite decisively over "OpenOffice". OpenOffice is still used a lot, but nowhere close to LibreOffice, especially when we add Linux distributions counts.