If the Chinese colonize, they would probably prefer abstract concepts for their important settlements/fortresses, expressing hope for how the place would turn out. Some examples from the fringe of OTL Chinese Empires:
迪化 Dihua [modern Urumqi] - 'To Enlighten (the barbarians)'
歸化 Guihua [modern Hohhot] - 'To Return and Convert (to civilization)'
撫順 Fushun [part of Shenyang] - 'To Pacify Smoothly'
As for middling/minor civilian settlements, one could assume a mix of geographical, transliteration and abstract names:
曹家堡 Caojiabao [Xining district] - 'Cao Clan Fort'
格爾木 Ge'ermu [Golmud, Qinghai] - Tibetan Na-Gor-Mo
遵義 Zunyi [Guizhou city] - 'Respecting Propriety'
And for really local areas (that have the chance to turn into big cities later on with industrialization), you have majority geographical designations, which might obviously be changed to more tasteful names
馬鞍山 Maanshan [Anhui city] - 'Horse Saddle Mountain'
青泥洼 Qingniwa [Dalian] - 'Green Mud Swamp'
As for exonyms, I think the following few points:
- The existence of gold on the American West Coast and in Australia will be factored into names (San Fran was the 'Old Gold Hill' while Melbourne was the 'New Gold Hill', and lots of Chinese were present at the BC Gold rushes).
Perhaps similar nomenclatures for ivory in Africa and spices in Indonesia (though OTL Indonesian exonyms seem primarily limited to navigational features e.g. 巨港 'Large Harbor' [Palembang], 錫江 '"Sek" River [Makassar], and 巴東 'East "Ba"' [Denpasar, Bali])?
- The greater the official Chinese influence, the less likely native transliterations would be used... frontier areas with little official influence could see local transliterations incorporated (like in OTL Taiwan: Keelung from Ketagalan, and of course the various Manchurian names in the NE)
- I would also note that a China with more overseas presence would also be more exposed to Western cartographical and etymological influence. Matteo Ricci's terms for many European countries (Spain, Portugal) as well as for the Atlantic and Pacific Oceans have survived to this day.