Wiki Wiki, a shuttle bus name at Honolulu Airport, is a great example of both alliteration and reiterative. Both of these have the function to please the ear or give additional emphasis.
In Chinese, there are many types, and my personal preference is to use iterative as a general term for all. Here are some examples:
1. Double sound word (叠音词) has a few types in Chinese. One is similar to alliteration (头韵 [tou2 yun4]) in English, i.e. initial rhythm or double initial consonant words (双声词).Examples in Chinese: 蜘蛛[zhi1zhu1] spider, 鸳鸯[yuan1 yang1] mandarin duck, 尴尬 [gan1 gan4] embarrass, 可口可乐[ke2kou3ke2le4]. There is also double final sound words (叠韵词 [die2yun4ci2])，骆驼［luo4tuo2] camel.
2. Reduplication(叠词 [die2 ci2])
AA 微微 [wei1wei1] slightly
AABB 高高低低 [gao1gao1di1di1] ups and downs
ABB 滑溜溜 [hua2liu1liu1] slippery
ABCC 喜气洋洋 [xi3qi4yang2yang2] full of joy
AAB 咯咯笑 [ge2ge2xiao4] giggle, laugh
ABAB 考虑考虑 [kao3lu:4kao3lu:4] think about it
ABAC 十全十美 [shi2quan2shi2mei3] perfect