It is possible to create a ticket whenever picklist field value on Organization changes.

Hello Bharadwaj G,

Triggers apply actions based on ticket changes. They execute when tickets are created or updated. Unfortunately, there isn't a trigger configuration that could automatically create a ticket based on a change in organization field values. 

Is there any alternative solution to accomplish this request in Zendesk?

There isn't a native way, unfortunately, creating a ticket when a value is changed in the organization field would have to be done manually.

Hi

You can explore using workflow rules or automation features provided by zendesk. These rules can evaluate the change in the picklist field value and trigger an action, such as creating a new ticket. 

Seeing above reply that it is not supported natively. I would suggest having a look at Exalate, it is an integration solution and based on triggers you can make new tickets. Theres a full httpclient built into it which will get the change of Organizations.

Hope to have helped