From my would-be current understanding
1) God's name does NOT need to be Mentioned AT THE TIME OF SLAUGHTERING.
2) God's name MUST be ***Remembered***before EATING THE ANIMAL
***the word used has the root of Z-K-R, thus you can remember God's name silently over the food, or outloud either way
(Does remembering God's name make a difference? Yes! (research :Masaru Emoto: Messages from Water)
*I think there are laws in the us which make Animals like cows have to be shot by a blow in the head before slaughtering to kind of render the animal brain dead
(This would render the animal unlawful since it has kind of been stricken/hit with an object, even if the animal is slaughtered after, the heart might not function properly to pump the blood out from the body, and the blood might retain in the organs, tissue/meat etc)
*Please only eat organic Kosher or Halal meat, that would be the best option.