Luiz
If the true drivers behind this change are because WMF senior management believe that the WMF is a competitor for Facebook or YouTube (as was in one of the marketing presentations), then the problem is their perception of the mission of the WMF, not the name "Wikimedia".
Surely WMF projects are in competition with commercial entities, and very successfully so? Wikipedia vs Britannica and Encarta; Wikivoyage vs Wiktravel; Wikinews vs Wikitribune; and so forth. We celebrate those projects successes ...
JPS