The account naming is really up to you. You could call it anything appropriate really. If this isn't a typical occurrence, just lump it into a misc account. The choice is also yours on putting to a misc vendor or a creating a unique vendor profile for them. One thing to consider is, don't mix 1099 vendors and non 1099 vendor transactions under the misc vendor profile, it will become a hassle. Also, don't mix 1099 relevant expenses (like contract labor) and non-1099 expenses (like a reimbursement) in the same misc account (accounts cant be both 1099 and non). Cleanest thing to do is likely to create an expense account called repair reimbursements, create a vendor for this incident, and in the create bill window, select the related customer in the Customer:Job column. If you don't see that column, right click and select customize columns. That should make things nice understandable without manual math or categorizing later.
