When you are ready to go to O365, you have to take into account that you’ll have your own address space, denoted by .onmicrosoft.com. But it’s not possible that two companies share the same tenant name. Also it is necessary to keep in mind, that it’s not possible to change the tenant name once it has been created, the only solution it’s to delete it by MS and create a new one, with all the configurations that this implies.
Furthermore, it is necessary to keep in mind that not only you will use your tenant name to distinguish companies, for example, brandname.onmicrosoft.com it also will be used for sharepoint, for example, brandname.onmicrosoft.com. So think twice the name of the tenant before assign it 🙂
For those cases, it is possible to check if the tenant name is available or not, for example, using the web http://o365.rocks you will be able to check the availability of the tenant name.
That’s all, hope this helps!