Asking for Title Change / Promotion

I recently helped with the planning, execution, and launch of my company's first ever tech touch / digital-led customer segment.

I'm currently a Client Outcomes Manager (our version of CSM) and have been for the 1.5 years I've been with the company. I now oversees the tech touch segment on top of managing customers day-to-day.

I'm looking to go to management to request a title change, but not sure how. Some titles I'm thinking of:

1. Client Outcomes Digital Led / Tech Touch Lead
2. Client Outcomes Manager & Digital Led Program Manager

For those of you who have been promoted before, how did you manage this conversation? What was your approach to management?