Do you mean setting stage name or task name value from a global property?
Manage Jenkins > Configure System > Global properties.

Setting Task Name from an environment variable, not a global property.
Thanks for the quick reply!

I'd also like to see this implemented. Just to be clear I'd like to use a build parameter as the value for the task name.

I can look in to it.
I have one question:
What should be the taskname value be if the build parameter is not set?

Good question! Either "" or maybe even "NONE|NOT_SET|NULL|". Thanks for looking into this, Patrik.

Hey Patrik,

I have a particular build scenario would make what I'm trying to do work (Note that my example is fictitious just to get my idea accross).

I have a matrix job with a 'User Defined Axis' named 'arguments.' Arguments has two values ('arg1' 'arg2'). The matrix job triggers a parameterized job (let's call this 'param_job') for each value of 'arguments' and passes the AXIS value as a parameter. 'param_job' has it's 'stage' set to 'deploy' and it's 'task' set to '$arguments'.

Right now when I look at the dashboard with the matrix job as the starting job it looks like this:

(matrix_job) -> param_job(stage: deploy, task: $arguments)

The issue here is that this doesn't show that matrix_job kicked of two builds of param_job.

Once this fix is in, should I expect the dashboard to show this:

(matrix_job) -> param_job(stage: deploy, task: arg1)
-> param_job(stage: deploy, task: arg2)

In response to your question about what to do if the param is not set... I would expect the value of task and stage to act as if the field itself was empty in the case that the param is not set.
Right now, I believe that task and stage default to the build name (not 100% sure) if the user leaves these fields blank.

Is there any possibility of implementing something like JENKINS-25377 (Ability to add variables to stage and task name) soon?

Fixed in:
https://github.com/Diabol/delivery-pipeline-plugin/pull/138

Released in 0.9.6