There's another thread about 'sun cream' and 'sunblock' sun cream, sun block and it seems that in AmE, the most common term is 'sunscreen' and in BrE - both 'sun cream' and 'sunscreen' are used. The W-R Dictionary, the OED and the Macmillan Dictionary include the word 'sun cream'. The Merriam-Webster Dictionary, for some strange reason, doesn't have the word. Most probably, it's because 'sun cream' is not what most Americans would call the 'lotion that you put on your skin to prevent sunburn by blocking out some of the sun's rays.', but it doesn't mean that 'sun cream' is not a word, they should've included it with '(Chiefly) British'.
Wikipedia shows there are quite a lot of names for the same product Sunscreen - Wikipedia .