Just a note. The MC's family name is Lin, given name Lu Xi. Her nickname Xiao Lu simply means 'Little Lu'. It can be combined with her family name to form 'Lin Xiao Lu'. You can refer to her by any of the above, but not 'Lin Xiao' like some of you do. It's the equivalence of calling Jane Doe 'Ja Doe'.
Tong Tong is probably a pet name too and not her actual given name.
Tong Tong IS her actual given name (it's two separate characters), but the nickname version is a repetition of the first character instead. But yeah you're right, Lin is the family name, Luxi is the given, and calling her Xiao Lu would be like calling her lu-chan if this was a Japanese comic