No, if HSV-1 spreads to the genitals, it does not become HSV-2. Both HSV-1 and HSV-2 are distinct viruses with different characteristics. However, either type of herpes virus can infect the oral or genital areas through close contact during sexual activity. The location of infection is what determines whether it's labeled as an oral (HSV-1) or a genital (HSV-2) case.
If you suspect you have contracted an STD like herpes, consider consulting your healthcare provider for proper testing and treatment options tailored to your needs.