Let's pretend it is an issue. How do you think you would solve it?
Actually, let's not pretend it's an issue, that's exactly what causes premature optimisation.
Here is the procedure to "solve it".
First prove it is an issue, via profiling. You've either done that and not posted results, or you haven't done that. Either way there is more work required at this step.
After that, your first attempt at a resolution should be to see how you can use strings less. E.g. if profiling showed that you had a bottleneck when comparing your string object IDs, then perhaps you could switch to using enumerations instead of strings. Or, if you're getting too many string copies, perhaps there are some critical places where the string is passed by value instead of const-reference.
The next thing to do is to look for a replacement that already exists. That may be in the form of a more-specialised part of the same library, or a whole other library. There is plenty that you can research.
Next, in considering whether to write your own replacement, you need to understand that in proceeding down the path of making your own, you are assuming that you can do a better job than the expert standard library writers. You are then assuming that you are in the top few percent of all C++ coders. Most people like to think that they are in the top few percent of C++ coders, but obviously most aren't. The experts are those who have first learnt to use existing tools very effectively (e.g. strings). One must learn why all the parts of the string class work as they do, in order to not fall into traps that others have already solved.
The final thing to understand is that even when there is a bottleneck, and even when you've done your best to optimise all related code as much as you can, there is always going to be a bottleneck somewhere. It's even possible that no matter what changes you make to a program, string handling could be such an unavoidable bottleneck (although that is generally unlikely, depending on what the program does).
You should probably read the thread, or at least my posts before writing such a long post telling me string is fine as is.
It was a proxy problem for a different problem I am having whose solution was similar.
EDIT: Good advice re: optimization however.