The reason some languages use "let name: type" instead of "type name" is to eliminate various ambiguities, for example C++'s most vexing parse, or the classic C typedef ambiguity where a statement like "X * Y" is ambiguous because it could be the declaration of a variable Y whose type is "X*" where "X" is a typedef, or it could be the multiplication of a variable "X" with a variable "Y". There are many languages where the "type" can be a fairly complex composition that can introduce ambiguities.

Modern languages use a type of syntax where all declarations start with an introducer, something along the lines of "let", "fn", "class", etc... in order to eliminate ambiguities as well as avoid the need for the parser to have potentially unbounded look-ahead.