Eu tive o mesmo problema, então eu pesquisei e encontrei isso em páginas de ajuda da Microsoft :
You can add multiple custom domains in all Office 365 subscriptions[...]
Esse artigo de ajuda parece possível, mas eles só falam sobre as versões comerciais e o Office 365 Home não é mencionado com uma única palavra - então continuei minha pesquisa, até mesmo entrei em contato com a Microsoft - eles não tinham ideia, mas Eu finalmente encontrei este post :
yesterday I called MS Support and the support engineer was discussing in the background with a colleague. Then he said that it's possible to use own domain with O365 Home... I just had to create a new account with my personal email adres/domain... after that I could order O365 and configure it with my own DNS domain name. Then after changing MX records with my hosting provider this would work for me.
anyway... I tried this anyway... I created a new account with my personal domain... then I ordered Office365Home hooked up to my paypal account....but in the end... no options for me to configure this. So I called back.... I got the same engineer... but then he said.. sorry, I don't have enough technical expertise, cause I'm a sales guy.... strange, because I tried to get tech help... The guy gave me a phonenumber to local (Belgium) Microsoft Tech support.... so I called the number. Then I got first or second line tech support on the line, so I expained the situation and the proposed option from his colleague. But I got a negative response.
No, sir, O365 Home does not allow you to use your own domain... why should it, there are not so many families using their own DNS domain, sir...
DUHH !!! What ? I don't understand their response... I times like this... people make their own family website... use a personal domain.... so I believe this is really a stupid reaction from a Microsoft Tech guy. Probably he has his own domain at home ;-) The only option is to choose for O365 Small Business and pay a lot more, because you need to pay for every user... every family member... so that would cost me at least 200€-250€ yearly.... please get serious ! so I give up.... Also Google Apps only has a business solution... also around 200€ yearly. Office365 Home... useless -> go for Office365 SMB... 2expensive ! I'll try again when Microsoft grows up and gets serious.
Afinal, não acho que seja possível, eu também encontrei algumas postagens no fórum e comentários em blogs e todos dizem que não é possível.