Go to IAM  → applications. There you will see the applications (without the IAM itself). Each application has a sequence number. IAM is 10. So if you want the application to be above IAM set the sequence to a number lower then 10. 
 

Additional info: https://docs.thinkwisesoftware.com/docs/iam_dev/applications.html

Thanks Erwin,

This at least explains the order in which icons are posted. And with the same sequence number probably alphabetical order is taken.

But this does not explain why in one environment IAM is opened an in another SF or another application. So where can I set this parameter?

For an application (this can be the SF itself or an application created with SF) this can be set in either user settings.
Users - user preferences - applications
or in  

User groups - group preferences - applications
 

If the tickbox load on start up is set this application will be loaded during startup of the iam if the sequence is lower then the sequence number of the application in the list. Otherwise it will be the top application in the list on the left that is loaded. 

Super, good to know.

But I have the impression that there is still another way to achieve this, as non of my environments have any of these preferences set.

What could be another way of achieving the starting up of another application than the one shown on top?

My colleague Erwin has explained all the possible ways of sorting start up applications. There is no alternative way.