Not offensive at all!!! It's actually extremely refreshing to see someone with this viewpoint. A lot of roleplayers try to co-opt DID and claim that you can actually make it voluntarily, and it's extremely harmful and toxic.
If your characters talk to you genuinely autonomously, I recommend seeing a therapist, as DID is caused by trauma prior to the age of 9 (or 11, in rare cases happening with comorbidities of ADHD and autism/ASD). Even if you don't remember the trauma (which is likely, as DID is extremely covert and is supposed to make you forget it), if your characters are talking to you, see a professional!
Also, there's a lot of fun and cool brain science on the weird things that roleplaying can do to your brain chemistry! I recommend this as a read on the topic! Actors getting into character has a genuine effect on electrical pathways in the brain very similar to the changes observed with identity disorders like BPD and PTSD, so it's fair a lot of people get them confused.
Also, as a psychology major and someone who's extremely well-read on the topic... don't worry - this is physiologically impossible
DID must be developed with severe trauma between the ages of 6 and 9 and cannot occur later in life! Anyone who tells you otherwise is severely misinformed at best, and maliciously trying to take advantage of you at worst.