Welcome. It's not clear from your description how you are accessing Companies House. If you still have problems you should report how you do this e.g.:
"I am going to the 'Explore this API' part of the search page (https://developer.companieshouse.gov.uk/api/docs/search/search.html), putting in 'walmart' into search term q and selecting my API key from the list. When I click 'try it out' I see ..."
"I am using the following command in curl: curl -uMY_APIKEY_FOLLOWED_BY_A_COLON: https://api.companieshouse.gov.uk/search?walmart and I get the following response: ... "
Note - Companies House recommend you don't write your real API key here - just put some text to show where you'd put it.
You've mentioned headers but you are showing some JSON. This isn't how http headers are normally passed or appear. Is this the output from some script or tool?
If you haven't already you might find it helpful to read the Companies House documentation:
To start with the Companies House authorisation guide may be useful.
Wikipedia and Mozilla (among many others) have helpful information about http basic authentication eg.
If you're new to REST APIs you might find some background information might be helpful. For example Mozilla has some useful information on http (e.g. what are headers, the body, parameters etc.)
...and there is a series of articles on REST at: