What is the action of writing with both hands simultaneously called?

I do not have enough reputation to comment, but you can always use the adverb ambidextrously plus the verb you need. For examples, you can go here: http://www.oxforddictionaries.com/definition/english/ambidextrous?q=ambidextrously#ambidextrous__10

There are clever and high-falutin' ways to convey the idea of writing with both hands simultaneously but employing the K.I.S.S. approach - Keep It Simple, Stupid! :-), why not just say that "he/she wrote with both hands simultaneously"?

To me, it is obvious that someone who is writing with both hands, simultaneously or alternatively, is ambidextrous so that word isn't really needed, is it?

I don't think a single word exists but some people afflicted by Kallman syndrome are affected by a condition called bimanual synkinesis in which the movements of one hand are mirrored by the other hand. So, analogously, I would use "bimanual writing", using bimanual as an adjective or an adverb, i.e., "He's bimanualy writing".

It is called writing. Writing does not imply using one hand or two hands. You can write in different ways so if you are using two or one hands it is still writing which is the act of enscribing information onto a medium. There are no rules for how the writing gets on the page.

One type of simultaneous right- and left-hand writing is called "writing in mirror images" or, more simply, "simultaneous mirror-writing." You can see a YouTube video of a woman performing this two-handed feat here.

For a fairly long article on simultaneous and nonsimultaneous mirror-writing (mostly the latter), see Robert D. McIntosh and Sergio Della Sala, "Mirror-writing" (October 2012), posted on the British Psychological Society's The Psychologist website. The part of that article most relevant to simultaneous writing is this excerpt:

Could deliberate mirror-writing offer insight into the nature of involuntary mirror-writing in brain-damaged adults?

We have recently had the chance to address this issue with Kasimir Bordihn (KB), a German artist, who has practised various forms of mirror-writing for more than 50 years. KB is a natural left-hander, schooled to write with the right hand, who ‘discovered’ mirror-writing aged nine, finding that he could halve his time writing lines by writing forward with his right hand and simultaneously backward with his left. He later practised and extended this technique, writing forward or backward with either hand, including vertical as well as horizontal flips, and incorporating these into a distinctive ‘mirror-art’ (see cover). We have begun a case study of KB’s abilities, which is providing clear support for the motor hypothesis of mirror-writing, and some less expected results.

Undoubtedly, when KB simultaneously writes the same words forward with one hand and backward with the other, he is engaged in simultaneous mirror-writing. But I'm not sure what you'd call his simultaneously writing half a line left-to-right with his right hand and writing the other half of the line right-to-left with his left hand. The article doesn't identify that skill by name.

If:

1. you are using a cell phone
2. you are using the thumb of both hands

then it is called texting.

Ambidextrous is the word for a person who can use both hands.

Wiki : Ambidexterity is the state of being equally adept in the use of both left and right appendages (such as the hands).

One can say, he is an expert in ambidexterity.

You can say, I am writing ambidextrously.

Synamphichiry would be properly formed from Greek, meaning something like "using both hands together at the same time" (syn- expressing "together at the same time").

Amphichirography would mean "writing with both hands".

Wonderful and creative question.

I remember the Rector at our Boys Home saying something similar:

Michelangelo was ambidextrous and often painted bimanually. The least we can do is to be two-handed in prayer. Manibus sedeas, Amen.

Bottom line is, IMHO, I believe we can use two-handed or bimanually.

PS: I just up-voted GMB's answer for originality and application of mind. It was GMB's answer that reminded me of this.

PS2: Our guidance counselor uses the term "bihemispherical activity" to indicate usage of both sides of the brain simultaneously. Not sure if this is a common term, though.

Ambitexterity. I just needed the concept myself and this is what came up.

A word for writing with both hands is ambidextrous and you are only 1 percent (of people?). Basically, if someone writes equally well with both hands, you may call them ambidextrous.