Well, whatever makes the flow of the text of the page most understandably. IF the logo is right next to the company name as text, then neither "Big Company Big Company" nor "Big Company Logo Big Company" is really best when spoken by a screen reader.
The requirement for alt tags is mostly for images as buttons:
<a href="page2.html"><img src="next.png" alt="next page" /> </a>
or other places where the image conveys real information, like graphs and charts.
Places where the image is merely decorative, a blank alt tag might be best.
Imaging an "About the company" web page, with all images with alt tags, being read aloud by a screen read. (Actaul text from exxonmobil.com: "About us- two workers on the Kizomba platform in Angola - We are the world's largest publicly traded international oil and gas company") Dragging the irrelevant detail from the image here lowers readability instead of raising it.