Does anyone know the name of this sort of English puzzle?

It's a rebus. It's also known by others names, picture puzzles, wordies, etc. You read the clues, words or pictures, to solve the puzzle which is usually a common idiom or saying.

This site has many rebus puzzles:

http://www.puzzlesurfer.com/

eg,

FUSS

nothing

= make a big fuss over nothing

Other good sites include:

http://www.fun-with-words.com/rebus_puzzles.html

http://kids.niehs.nih.gov/braintpics.htm

Smith is the main straight forward final call as a results of fact it ability a individual who works in metals, so this is truthfully a depiction. this is derived from some time past whilst human beings could say "Bob the Smith"(as in blacksmith, or coppersmith) and has been shortened over the years to "Bob Smith" meaning Bob the Smith.

sometimes called a rebus or dingbat