Well I am going to say "no", not necessarily.
Since the primary actions are to control the aircraft height/heading (asymmetry), understand if the failure is catastrophic (fire or bits flying off) or not and then go through re-start drills or shutdown/feather drills A/R then,
Secondary actions are to "secure" the live engine;
Then, and only then would you decide to call someone with a "mayday".
As, by then, you won't necessarily know if it is contagious 
you might require an expeditious landing/return to base.
If it is "obviously" only one-out you don't need to immediately go to a "mayday" unless you can't maintain height (and need to) or have some secondary issue such as damage from debris, ice, or you suspect it might be fuel related or something that might affect the live one.
When it happened to me it was not a "mayday", we were still on frequency with departure aerodrome and asked for an expedited return.
No drama.
As PIC you would know what systems were affected by which engine inop, so it is your call. Always.