Is it legally punishable to use the name of a product (ak-47, m16, etc.) in a video game without permission?

You should consult a lawyer, but the AK-47 and M16 are government products, so using their names may not be an issue, you might even argue for historical verisimilitude.

AK47 isn't a brand name, its basically a shorthand description of the weapon. It stands for Avtomat Kalashnikova 1947 (Soviet-Made 7.62mm Assault Rifle)

M16 is a similar story the M stands for model as far as i can tell.

When you see the letters AR next to each other as in SCAR-H or TAR it usually stands for Assualt Rifle.

I suggest reading about Electronic Arts usage of real life weapon names in their titles. They faced the exact same situation and were paying royalties for the right to use the trademarked names to the weapon manufacturers until they decided to change their policies.

For example, AK-47 and M16 are not trademarked names but AR-15 is so you'd have to check on a per gun basis.