In Salesforce there is a field called “Task Subtype” (in the Task object) which dictates the icons in the Activity Feed. The possible values are:

• Task [Task Icon]
• Call [Phone Icon]
• Email [Letter Icon]
• ListEmail [Stacked Letters Icon]
• Cadence (if Sales Engagement is being used) [Task Icon]

A similar field exists on Events appropriately called “Event Subtype”

• Event [Calendar Icon]

Both fields cannot be edited, but can be set on record creation. To answer the title question, no the value cannot be changed. An alternate could be cloning the activity, with the exception of the Task Subtype field and recreating with the desired Task Subtype afterward deleting the original record.