MCI error victim

I suffered the similar case since May 2024. HMRC app update me as MAHTAB CATERERS LTD has been my employer. I called HMRC in June, a staff told me wait for 3 weeks to fix the MCI error. I got another answer in next call after month that they have nothing to do but wait. My last call in Oct, I was told my MCI error would be fixed on a specific date, but the error is not fixed after 2 months passed. It is surprising that HMRC seems no idea on the investigation. It suppose only employer or its agents can file a new employment to HMRC. If there is no evidence of this filing, does it mean HMRC made this mistake internally? I suggest all victims to builld a log without personal details, e.g. fake employer name, date, what/how to report, what is HMRC reponse, how and how long to fix