Illusionary mask and Meddlin' mage

[Polynomial P]

If I put Meddlin' mage into play with an illusionary mask, do I get to name a card when I flip meddlin" mage? It is not a triggered "when this comes into play" ability, so I am not sure if it acts the same as Phyrexian dreadnought.

Meddling Mage
WU (2), Creature - Wizard 2/2
As Meddling Mage comes into play, name a nonland card.
The named card can't be played.

Illusionary Mask
2, Artifact
: You may put a creature card with converted mana cost X or less from your hand into play face down as a 0/1 creature. Put X mask counters on that creature. Play this ability only any time you could play a sorcery. The creature's controller may turn the creature face up any time he or she could play an instant by removing all mask counters from it. This effect ends if the creature is turned face up.

Also, is flipping the card from illusionary mask considered a non-stack action in the way that morphing a card is? Would my opponent get a chance to respond to me removing the mask counters from the face-down card?

[Anusien]

If I put Meddlin' mage into play with an illusionary mask, do I get to name a card when I flip meddlin" mage? It is not a triggered "when this comes into play" ability

You hit the nail on the head.  Meddling Mage has a static ability that has an affect as the card is coming into play.  Since it is not Meddling Mage as it comes to play, you do not name anything.  This is similar to Vesuvan Shapeshifter becoming a Meddling Mage later.

[kirbysdl]

On a related note, a Mage played as an instant (Aether Vial/Aluren/etc.) cannot affect a spell on the stack, right?  For example, if someone plays Wrath of God, and I Vial in a Mage naming Wrath in response, the Mage will simply die with everything else when Wrath resolves, right? 

[Clariax]

On a related note, a Mage played as an instant (Aether Vial/Aluren/etc.) cannot affect a spell on the stack, right?  For example, if someone plays Wrath of God, and I Vial in a Mage naming Wrath in response, the Mage will simply die with everything else when Wrath resolves, right? 

Correct.  Meddling Mage's ability prevents the named spell from being played.  The Wrath of God already on the stack has already been played (just hasn't resovled yet), so Meddling Mage can't affect it (and will likely be destroyed by it)

Also, is flipping the card from illusionary mask considered a non-stack action in the way that morphing a card is? Would my opponent get a chance to respond to me removing the mask counters from the face-down card?

It does not use the stack, your opponent doesn't get any oppurtunity to play anything until it's already face up

[andrewpate]

On a related note, a Mage played as an instant (Aether Vial/Aluren/etc.) cannot affect a spell on the stack, right?  For example, if someone plays Wrath of God, and I Vial in a Mage naming Wrath in response, the Mage will simply die with everything else when Wrath resolves, right? 

Correct.  Meddling Mage's ability prevents the named spell from being played.  The Wrath of God already on the stack has already been played (just hasn't resovled yet), so Meddling Mage can't affect it (and will likely be destroyed by it)

If you have heard reference to Meddling Mage being used in this way, it was probably regarding the interaction with Madness, for example when Pierre Canali famously countered a Circular Logic with it in the Top 8 webcast at Pro Tour: Columbus.  This only works because Madness is partially a triggered ability; the AEther Vial can be activated after the discard but before the Circular Logic actually goes on the stack.