Is merely uttering the name with the intention of conditional Dhihar, for someone who suffers from obsessive-compulsive disorder, considered a Dhihar oath or not? And what is the advice for dealing with the obsessive thoughts of divorce and Dhihar?

We ask Allah to grant you healing. You must strive against yourself to seek Allah's help and supplicate to Him, then completely disregard the waswas (whispers); because what you mentioned does not constitute divorce or ẓihār, and it is from the whispers of Satan. Therefore, the effective remedy for this is to completely ignore them. Whoever pays no attention to them, they will disappear, and whoever listens to them, they will increase until they drive him to the brink of madness, as stated in the Sahihayn that whoever is afflicted with waswas should seek refuge in Allah and desist. In addition to that, continue psychological treatment with trustworthy Muslim psychiatrists, as it has a beneficial effect. You can also consult the counseling section on the website.