the sunlight that streams into a room through the window

Solution 1:

These are also called shafts of light

Shaft: 5. Something suggestive of a spear or arrow in appearance or configuration, as: a. A ray or beam of light.¹

From Shakespeare: The Two Traditions:

A shaft of light falls on the scene as the young-looking Fortinbras enters...

^{1_{American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2011 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.}}

Solution 2:

How about sunbeams or rays of sunlight? The meaning of these terms is a little broader than the specific context you're talking about, but I can't think of a better word.

Sunbeam here is defined as:

a beam, ray, or stream of sunlight.

Solution 3:

Crepuscular ray, while technically a reference to twilight sun, is often used figuratively for rays of sunshine in other situations.