A passage from the story itself illustrates Rikki-tikkis' curiosity better than anything I could say...
"He nearly drowned himself in the bath-tubs, put his nose into the ink on a writing table, and burnt it on the end of the big man's cigar, for he climbed up in the big man's lap to see how writing was done. At nightfall he ran into Teddy's nursery to watch how kerosene-lamps were lighted, and when Teddy went to bed Rikki-tikki climbed up too; but he was a restless companion, because he had to get up and attend to every noise all through the night, and find out what made it."
Her name is Rikki Chadwick.
Rikki Chamberlain's birth name is Rikki David James Chamberlain.
Rikki Anderson's birth name is Tericka Dye.
Rikki Marin's birth name is Darlene Morley.
Rikki Love's birth name is Joy Miketzuk.
Rikki Rockett's birth name is Ream, Richard Alan.
Rikki Fulton's birth name is Fulton, Robert Kerr.
Rikki can be a unisex name and is derived from the name Richard. It is more commonly used as a boy's name, but it can also be used for girls.
Rikki Lee Travolta's birth name is Richard Lee Travolta.
Rikki Arnot's birth name is Rikki Lee Arnot.
In the story "Rikki-Tikki-Tavi" by Rudyard Kipling, the father's name is Darzee. He is a tailorbird who warns Rikki-tikki about the cobras Nag and Nagaina.
the word Rikki means peaceful leader. i would know!!