No. Due to how the pathogens that cause a particular STD cannot survive in inanimate surfaces, it is implausible for one to contract an STD from a surface that once came into contact with an infected individual. In most cases, direct contact with infected bodily fluids is the method that has the highest potential to induce transmission of the pathogenic microorganism. Nevertheless, it is still a practical matter of hygiene to ensure that any surfaces you come into contact with are clean and appropriately sanitized to avoid the transmission of other microorganisms that may not necessarily induce an STD.
If you didn’t find what you needed, these could help!