If a third party buys something for the company under their own name (e.g. a domain), how is it claimed, and do we reimburse them in cash once the invoice is submitted?
This is treated as an expense claim where a company purchase paid personally by an individual (employee, director, or shareholder), which the company is expected to reimburse.
The invoice/receipt is submitted showing the purchase, it's recorded as a company expense, and reimbursement to the individual is via bank transfer or however the company normally settles expense claims