recently a bug in core was fixed (deltachat/deltachat-core-rust#5585) to include the overridden sender name property if present also for self/outgoing messages (the names with the ~ at the front) Delta Chat desktop should display the author/sender title in the top of the message bubble even for self messages if the overridden sender name property is present, this is already done by android on deltachat/deltachat-android#3056

It should be displayed when present, it doesn't matter if chat is a group or 1:1, based on the raw RPC API I think the property to check is MessageObject.overrideSenderName in the TypeScript bindings but not sure.

Delta Chat itself doesn't allow to set overridden sender name for a message from the clients, but it can happen that it is set by another email client of the user, for example by DeltaLab's recent communities support

for context, this is how it should look a message from self that has an overridden sender name set: