Not really. If they carry on down this route and keep the internal migration to this region up, they will be a small minority eventually. Just as they have in Tibet, the Han are in control and are playing to win.
The Han Chinese are unofficially banned from migrating to the Tarim Basin, or the core Uyghur area. They mostly settle in Dzungaria, which was never Uygyur majority in terms of history, but previously populated by Dzungars, a group of Oirat Mongols who were genocided by the Qing forces, afterwards which they settled Uyghur, Hui and Han in those territories.
I'm not sure if they are officially banned but they rarely venture out to the Kashgar region. Xinjiang has primarily two different zones, there is Beijiang (Northern Xinjiang) centered around Urumqi where there is a lot of Han influence, the Uighurs and Kazakhs there are also pretty sinicized. And then there is Nanjiang (Southern Xinjiang), centered around Kashgar which is the historic Uighur stronghold, that region is still very strongly Uighur.
Anyways, as for the rules banning names, it's stupid, but I guess they are paranoid about the rising extremism.
China's government really only cares about religion if it infringes on their sovereignty. They have anti-Islamic laws for the Uighurs, but not for other Muslim groups like the Huis or Salars or Dongxiang, etc. Because the Uighurs are the only ones actively agitating for independence.
Same with underground Christian churches, state approved Churches are allowed to thrive, but underground churches are cracked down on, because they underground preachers often lambast against the government, so they are a threat.
Tibetan Buddhism is also oppressed, because the Tibetans have an independence movement. There is a lot of government surveillance of Tibetan monasteries, but less so outside Tibet SAR (there is a huge Tibetan population in the neighboring provinces and they have much less controls because there is little support for subversive activity in those regions).
Banning Baby names is too extreme. What is China doing?
Well, China is the only civilization to have successfully assimilated the Jews. LOL
There is an ancient community in Kaifeng but I think they lost touch with their roots long ago, but are now rediscovering it.
https://www.youtube.com/watch?v=6EuZNnsZXSg