I’m just another user here but if you didn’t find a solution already did you read the following:
I guess you’d need to be more specific about the actual issue you’re having so I can only offer general points:
No specific “previous name search” yet as far as I know. To search for a previous name you could do a normal company search, then look in the “snippet” field(s) returned - matches on previous names would appear here.
there have been some issues with previous names / dates for these not being correct (search forums to see these).
CH API only gives data on closed companies less than 6 years old.
If you think you should find a company but can’t see it in API, try checking on WebCHeck and / or the companies URI if you know the company number (example URI). These have data going back further.