What Is The Name Of The Three Dots At The End Of A Sentence?

The three dots that are at the end of the sentence are called ellipses. It is used when a sentence, a statement or speech can be understood without actually saying it. Ellipses are marked either by a row of three *** or three (…) most commonly they used by marking (…)

In the following examples the ellipted material is given in brackets. (1) 'Would you like to have dinner with us?' - 'Yes, I'd love to' [have dinner with you]. (2) 'What did she tell you?' - [She told me] 'That she was busy.' (3) I should have finished that paper, but I haven't [finished that paper].

These stops are also known as Period of Ellipses, suspension points, Points of ellipses or simply DOT-DOT-DOT.

It is sometimes used to designate an unfinished thought. Sometime ellipses are also used to end a sentence without revealing the true intentions or meaning of the sentence.

Jdcengr has a correct observation.  It replaces words which are either obvious, redundant, or unnecessary in the sentence.  I would add that it can be anywhere in a sentence - at the beginning, in the middle, or at the end of a sentence, and, usually, are not enclosed in parentheses. .