a diagnosis plays a large role in treatment options. DID however is rather statistically uncommon, which may be why your GP seems to be going along with the current treatment regimen/diagnosis. I think it's up to you if you want a second opinion. There is no harm in seeking a confirmation of the diagnosis, but I would not suggest seeking out a particular diagnosis.
How is treatment going now? Do you feel like you are improving? Are there symptoms that need to be addressed? Do you have trust in the rest of your treatment team? If there are still things bothering you that you feel need addressing, it may be worth bringing up to them.
Talking to your insurance company might be a good way to get a referral for a second opinion if your GP is not willing to give you a name. Be up front about the fact that you are looking for another opinion when you do see the person. A dialogue about why you think your current diagnosis is incorrect may be a valuable one to have (both with your current treaters and the second opinion).
Sometimes the diagnoses we are given do not feel "right" but may still be valid based on what is being presented at the time...