use a company name and a separate ac when I need to employ others (about 2-3 times a year)
Eh? If you're a sole trader, then surely you're still a sole trader, even when you're Eviljoe trading as joe's Pink Knickers or whatever?
As for your current cusotmer/client (be careful of using the word employer if you don't mean that – could have negative tax/NI consequences), I suspect the only reason they require details of a company name and number and tax numbers is for their internal reporting requirements – just tell them that you are a sole trader, and don't have a VAT number etc. because you're below the threshold.
Sounds like some idiot who has to fill out a form.
Is it really worth going through the hassle of setting up a company with companies house with so little going through the books, and the company rarely being used?
Probably not.