Beginning programmers ask this question regarding every language. There are a group of computer languages for which the answer to this question is "yes". These are dynamic, interactive languages, like BASIC, Lisp, Ruby, Python. But think about it: Variable names only exist in code, for the convenience of the programmer. It only makes sense to define a new variable while the program runs if there's a person to then subsequently type the name of the variable in new code. This is true for interactive language environment, and not true for compiled languages like C++ or Java. In C++, by the time the program runs, and the imaginary new variable would be created, there's no one around to type code that would use that new variable.
What you really want instead is the ability to associate a name with an object at runtime, so that code -- not people -- can use that name to find the object. As other people have already pointed out, the map
feature of C++'s standard library gives you that ability.