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 ...