For DevOps Team : Whom should i assign the ticket when more than one person is working on it ?

Why would you assign a ticket to anyone?  Shouldn't the people doing the work take care of the ticket management?  In a self-managed, self-organizing team those kind of decisions are made by the people doing the work. 

It looks like you want to work around the limitations of the tool. Without knowing what tool(s) you are using, it's almost impossible to give a good answer. You may not even need to assign the ticket to anyone.

For DevOps Team : Whom should i assign the ticket when more than one person is working on it ?

If you've really got a team, within which teamwork is being demonstrated, wouldn't you expect multiple people to be working on a requirement? Isn't it a bit artificial and counterproductive to pretend otherwise?

Thomas, We use Jira - Atlassian for ticket management. It's a day-to-day DevOps task completed by 2-3 team members based on their shifts and week offs and we close that ticket once the sprint ends. I think it's not good to create multiple tickets for the same task for 2-3 team members; each wants a separate ticket for them. So I got stuck here and don't know how to handle this situation!

And we are not there yet, I can't let the team have the ticket management because in that case, they will end up assigning nothing to them.

When my team had any huge task to be done by multiple engineers, we would break down and identify each sub-task within the huge task. This allows us to clarify what's to be done and understand why the task needs multiple people to handle it. 

A few things come to mind:

• Can you make the work smaller? Can you decompose the work into smaller units that a single person can do in less than a shift?
• Can you use subtasks? If there are discrete steps that need to happen, decompose the larger work into subtasks and have people take on subtasks. I'd want to make sure that the subtasks are things that an individual could reasonably start and finish in one shift.
• Do you need multiple people working on the same item? Even if it takes more calendar days, do the hand-offs between people make sense? Hand-offs introduce waste in the form of needing additional knowledge transfer. By having one person complete the work, you don't need to transfer knowledge about the state of the work or decisions made among individuals until the work is done.