Is there a way to provision a SQL Server virtual machine on azure with a named instance or does it always install the default?
Not with the pre-built images.
If you provision your own VM and use IaaS agent extension you can use named instance.
Can I install a second instance of SQL Server on the same VM? Can I change installed features of the default instance?
Yes. The SQL Server installation media is located in a folder on the C
drive. Run Setup.exe from that location to add new SQL Server
instances or to change other installed features of SQL Server on the
machine. Note that some features, such as Automated Backup, Automated
Patching, and Azure Key Vault Integration, only operate against the
default instance, or a named instance that was configured properly.
Can I use a named instance of SQL Server with the IaaS extension?
Yes, if the named instance is the only instance on the SQL Server, and
if the original default instance was uninstalled properly. If there is
no default instance and there are multiple named instances on a single
SQL Server VM, the SQL Server IaaS agent extension will fail to