How did Rikki get his name in "Rikki-tikki-tavi? What literary term is this?

Rikki got his name from the sound he makes, an example of onomatopoeia.

Onomatopoeia is a sound device where a word is used that makes a sound.  The words are usually spelled to represent the sound.  In this case, the sound is the war cry of the mongoose.

His eyes and the end of his restless nose were pink; he could scratch himself anywhere he pleased, with any leg, front or back, that he chose...

Rikki got his name from the sound he makes, an example of onomatopoeia.

Onomatopoeia is a sound device where a word is used that makes a sound.  The words are usually spelled to represent the sound.  In this case, the sound is the war cry of the mongoose.

His eyes and the end of his restless nose were pink; he could scratch himself anywhere he pleased, with any leg, front or back, that he chose to use; he could fluff up his tail till it looked like a bottle-brush, and his war-cry, as he scuttled through the long grass, was: ``Rikk-tikk-tikki-tikki-tchk!''

Since Rikki is an animal, it makes sense that he might get his name from the sound of the noise that he makes.  A mongoose is a very brave creature, and according to Kipling a mongoose is also incredibly curious.  While snakes are the natural enemy of the mongoose, Rikki is not even afraid of the cobras.

He was afraid for the minute; but it is impossible for a mongoose to stay frightened for any length of time, … and he knew that all a grown mongoose's business in life was to fight and eat snakes.

Rikki makes his war cry when he is on the hunt.  Throughout the story, Rikki successfully kills three snakes.  He kills the small but deadly Karait first, and then follows it up with the successful deaths of the two cobras, Nag and his wife Nagaina.  He protects the humans that are living in the house, and the other animals in the garden.

Personification is often used in stories that serve as fables.  Animals are given human traits and values.  In this story, we learn the effects of colonialism through Rikki and the cobras.  Rikki comes in and believes he owns the place.  His war cry is the death knell to the original inhabitants of the garden, the cobras.  While we may cheer for the mongoose, it is important to remember that the snakes were there first.