Iona, Shield of Emeria

[Shipp]

Can my opponent respond to me playing Iona by casting swords to plowshares on it before I get to name white?

[H]

No, abilities that say "As X enters the battlefield..." do not use the stack and can not be responded to (As being the important differentiator).

[PirateKing]

They can respond to Iona being cast, but she will not be on the battlefield, so not a valid target for Sword to Plowshares.
Once Iona is on the battlefield, the color white has been chosen, and your opponent's can't cast Swords to Plowshares.
So, no.

[Shipp]

Awesome, thank you

[Technics]

In a similar regard, Phyrexian Revoker works the same way, and you can not use something on board to kill/bounce it prior to him naming (so your Seal of Fire is useless if he names it).

[kavaki]

Yes, as it uses the wording "As". The card is already named by the time any player would get priority with it on the field.