Are commercial aircraft required to have the model number painted on them?
Every aircraft I have flown had a data plate mounted somewhere in the outside, showing the make, model, serial number, and the year of manufacture. You probably can't see it unless you're 3 feet away, but it's there.
The relevant regulation in the US is:

§ 45.11 Marking of products.
(a) Aircraft. A manufacturer of aircraft
covered under § 21.182 of this chapter must mark each aircraft by
attaching a fireproof identification plate that—
(1) Includes the
information specified in § 45.13 using an approved method of fireproof
marking;
(2) Must be secured in such a manner that it will not likely
be defaced or removed during normal service, or lost or destroyed in
an accident; and
(3) Except as provided in paragraphs (d) through (h)
of this section, must be secured to the aircraft fuselage exterior so
that it is legible to a person on the ground, and must be either
adjacent to and aft of the rear-most entrance door or on the fuselage
surface near the tail surfaces.

and

§ 45.13 Identification data.
(a) The identification required by § 45.11 (a) through (c) must
include the following information:
(1) Builder's name.
(2) Model designation.
(3) Builder's serial number.
(4) Type certificate number, if any.
(5) Production certificate number, if any.

Here's an example from a Stinson 108: