You must detach the acquired accounts from the original domain before adding it to the new domain. This may disrupt the flow of email several times in the progress
If changing usernames too, a mailbox identity can be changed and requires a reconfiguration of each outlook client.
Passwords will not be migrated. If using AD Connect (DirSync), any changes will require credentials be upgraded too.
This is not an easy process. There are 3rd party tools that you can pay for to make it a little easier.
This link gives you a picture of what you might need to consider before tackling this on your own: https://www.freeviewer.org/blog/combine-two-office-365-tenants/