Root cause analysis is part of Problem Management activities.
There are several techniques:
Pain value analysis
Kepner and Tregoe
More on Problem Management in the article:
ITIL and ISO 20000 Problem Management – Organizing for problem resolution https://advisera.com/20000academy/blog/2014/07/29/itil-iso-20000-problem-management-organizing-problem-resolution/
ITIL Problem Management: getting rid of problems https://advisera.com/20000academy/blog/2013/08/05/itil-problem-management-getting-rid-problems/
2) Does the organization must have a designated incident management team?
I think you should have designated Incident Management team. There are many advantages, but here are more details:
ITIL Incident Management benefits – Simple explanation for your top management https://advisera.com/20000academy/blog/2015/11/24/itil-incident-management-benefits-simple-explanation-for-your-top-management/
ITIL Incident Management https://advisera.com/20000academy/knowledgebase/itil/-incident-management/
as well as our free webinar
ITIL Incident Management Process Demystified https://advisera.com/20000academy/webinar/itil-incident-management-process-demystified-free-webinar-on-demand/