There are a few different cases to consider. First of all, there is the question of whether a journal's policy even allows for signed reviews. I think that most journals do not have an official policy about this. However, if there is a strict prohibition against non-anonymous reviews, then the editor should remove the identifying information before sending the report on to the authors (and any other relevant parties, such as other referees who are working on the same paper).
In the more likely event that signed reviews are not outright forbidden, then editor should look at the additional question of whether the referee really intended to make their identity known. From the report alone, it may or may not be clear whether a referee is intentionally choosing to dispense with anonymity. If there is just a signature at the end of the report, the reviewer might have added it out of absentmindedness. If the situation is unclear, the editor should check back with the referee, to see whether they actually intended to include their name before passing that name on.
However, I have seen one review that concluded with:
I choose to sign this review.
In that case, it was quite clear that the reviewer (who was both a very senior person and giving a positive report) was not worried about maintaining anonymity. In a clear-cut situation like this, a referee can simply send the authors the report without any additional concerns.