Short or Long Function Names?

I am frequently in doubt should I use short or long variable names. In some circumstances, long names look better - for example, when I start using some function, it is easier to remember long name. And it is especially easier to explain programs to other people if functions have long, descriptive names.

On the other side, after some use, long names are counterproductive - code is longer, and it takes more time to write it.

Recently, I came to idea to define functions with two names, long and short one. I think it is not accidental that we usually have two names - original, long name - and then shorter name, nickname, acronym or abbreviation. Look at this:

Philosophy Doctor --> Ph.D.
United States of America --> USA
Robert --> Bob
In my humble opinion --> IMHO

It cannot be accidental, right? So, now, I'm in experimental period of defining double names. For example, I have Lispy name string-append and Perly $+, identity-function (lambda(x)x) and IF, identity-macro (lambda-macro(x)x) and IM.

So far, so good. I'll report experiences in future. Try it, maybe you'll like it also.