What is the name and preparation style of this type of tofu?
This is Bì Cuốn Chay (bì = skin , cuốn = roll , chay = vegetarian). The meat version is Bì Cuốn, using pork + pork skin + roasted rice powder (thính) as the main ingredients. 

To make the vegetarian dish, you can either  use gluten meal (mì căn) widely available in all East Asian groceries, or use tofu as you mentioned. The gluten meal is sold either uncooked or seasoned &amp; cooked.  I'd rather use the uncooked version &amp; season it to taste as most cooked versions have heavy Chinese five spice seasoning &amp; oil that don't go well with the Viet flavors on this roll. 

The tofu is actually very simple and is nothing special. You can get a couple blocks of semi- firm or firm tofu, slice them to about 1 inch thick or slightly less, leave them to dry for a couple hours, then fry them brown. You can season them with a bit of soy sauce if desired or season after frying. Cut them to the desired pieces as in the pictures, coat them with thính and use the other ingredient to make your roll. 

You can buy thính in a bag or small jar at the store, or simply roast some rice on a pan until brown, then use a grinder like a good pepper grinder ( be sure to wash all the pepper smell out first) and grind the roasted rice to a powder. I like to roast my own because the freshly roasted rice smell way better than store bought. Once done with the rolls, you can use nước mắm chay (vegetarian "fish" sauce) to make a dip sauce. 

Here is a YouTube video for the tofu version (in Vietnamese)

Wish you success &amp; Enjoy!