When are the single square brackets in bash
The square brackets are a synonym for the test command. An if statement checks the exit status of a command in order to decide which branch to take. grep -q "$text" is a command, but "$name" = 'Bob' is not--it's just an expression. test is a command, which takes an expression and evaluates it:
if test "$name" = 'Bob'; then ...
Since square brackets are a synonym for the test command, you can then rewrite it as your original statement:
if [ "$name" = 'Bob' ]; then ...
An if statement executes a command and executes the then part if the command succeeds, or the else part (if any) if it fails. (A command succeeds if it exits with a status ($?) of 0, fails if it exits with a non-zero status.)