If Domain2\Myname later wants to store his profile on the same server, he will have a problem. So, if Domain1\Myname has explicit full control permission to the ...\Myname folder, then this profile belongs to me and not to Domain2\Myname.
The way that a user’s profile folder is named depends on the circumstances in which it’s created.
The user My Name (with user name Myname) with an account in Domain1 will store his profile in one of two places: \RDS-Roaming-Profiles\ Myname or \RDS-Roaming-Profiles\Myname. The best case is to add the domain name to the profile path; this disambiguates the path when there are two (or more) users with the same name living in different domains.
For example, in a large corporate network, you might have Domain1\ Myname (that’s me) and Domain2\Myname (some other user).
When Domain1\ Myname logs on to a legacy terminal server the profile created for him will be ...\Myname. But in this case, how do you know which user this particular profile belongs to? When the User Profile Service creates a new profile, it gives full control to the user whom this profile is created for.
Again, it’s always best to include the domain name in the profile path so that two people with the same user name with accounts in different domains can store their profiles in the same central share.
When you’ve set up the profile location, configure the user account to use roaming profiles.
This process varies slightly for profiles used with RD Session Host servers and for profiles used with pooled and personal VMs.
You will see these differences as you step through this process.
It’s easiest if you configure this via Group Policy, but you will also see how to do it on a per-user basis.