How might you record a loan from directors to the company in the books?
From my perspective this is an investment into the company which I hope will be refunded when the company makes profits.
The way I've been recording this in the company accounts is as a long-term liability on the balance sheet. Is this appropriate? Is there a standard name for this?
("director's loan" seems to be used for the other direction, company giving a loan to a director).
It depends whether the director is also a shareholder or not. If the director is a shareholder, usually this is recorded as a "shareholder's loan." You are correct in thinking that a directors loan is usually a loan from the company to a director, a transaction which is subject to high scrutiny due to insider dealing and very regulated in corporate law.
Shareholders loans, on the other hand, increase the basis that any shareholder has in their stock in the corporation, which is effectively like a capital contribution for tax purposes. There is a slight difference between capital contributions on the books for tax purposes and shareholders loans, but they have the same affect on your basis.