Because of categorical perception (as defined on the https://dictionary.apa.org/categorical-perception page), there's no general agreement on the "correct" way to pronounce a non-English name within English communication to a mostly English speaking audience. Some people argue that the right approach is to always use the closest equivalents within the English phonemic inventory. In this view, it's incorrect to suddenly shift English speech into the phonemic inventory of a name's origin. Listeners, on average, simply can't and won't hear the name consistently, and thus communication is less effective. The opposite view is that this is just another example of cultural arrogance, and it's best to shift out of the English phonemic inventory whenever that's reasonably possible. (For example, in this view, the shift should occur when a name is part of news coverage, and the speaker had an opportunity to learn the phonemes of the original language in advance.)

This isn't specific to English: it's the general question of whether a speaker should always stay within the phonemic inventory of the communication's main language.