why do we call lone *pairs*? According to VSEPR theory, molecules adjust their shape to minimize the effect of repulsion.

Suppose I take the structure of $\ce{ClF3}$. It has three bond pairs and two lone pairs.
So to minimize the repulsion it gets T-shape (the two lone pairs are at corners of a trigonal bipyramidal shape).

But my doubt is why do we call two lone electrons a lone pair? I mean, if we keep a lone pair at some point in a molecule, how can two lone electrons be so near? Why don't we take electrons individually but always lone pairs?
We call them "pairs" because there are two electrons in each grouping. Why are there two instead of three or just one?

Spin and orbital energies.

One electron up and one electron down, in order to have all electrons in the lowest energy orbital available. Having them separate is a vastly higher energy state for the particles as a whole.

If you have not yet studied orbital theory - your question will be answered in much more depth when you do.