21:05 Jan 20 

Home office means an office at home if you are working from home for example. Capitalized, Home Office, it is the Ministre de l'intérieur. Danger, faux ami!

"Head office" is the main business address. It is sometimes, although not always, the same as the "registered office", the one registered as the official address on the companies register. The latter, the reigstered office, is often at the company's accountant's office. The latter is more often used for service of legal and accountancy than the head office. This last para is just FYI...

I spent lots of time as an articled clerk, a litigation assistant and in other legaly beagley jobs running around filling in forms and doing company searches checking out dusty microfiches for all this sort of stuff! (Long live internet!)

19:20 Jan 20 

Be that as it may, "election of domicile" really does not appear to be an English term. I haven't found a single native English document using it. Have you?

19:18 Jan 20 

BTW, many "UK sites" do not use ".uk" ;)

18:12 Jan 20 

A number of entries in the KudoZ archives. The more heavyweight dictionaries often have this term too as it is quite a standard legal and indeed business term. Reminds me of all the form filling and legwork done in my distant days of articled clerkship!

16:46 Jan 20 

A search for "election of domicile" on UK sites gives you 12 results. Not exactly convincing IMO.