I can't believe we're really talking about this. No one really cares; I'm sure by Thursday even cable news will have moved on to something else. But since Neil and I are charter members of the "people who constantly have to teach others how to spell and pronounce their last name" Facebook group, let's have at it.
First off, let's note the tremendous irony of using "Niedermayer", which is probably German but certainly not English, as the reference for the "English" pronunciation of "Sotomayor".
Second, other than Sotomayor herself, no one's rolling the final 'r' or putting a partial glottal stop after the 't'. Plenty of Latino surnames have already suffered a similar fate. The majority of three-syllable words in English place the accent on the first syllabble, but no one calls the Yankees' third basemen "Alex ROD-ree-gez". But no one rolls the 'r's or pronounces the 'g' a bit closer to a 'k' sound. As is often the case, we've adopted the Spanish-language emphasis but Americanized the pronunciation. Her name's pronunciation as already been partially Anglicized.
Third, let's find something else to talk about. Please.