You are possibly thinking of the AXA logo
axa
A logo with a blue background and white letters could refer to several brands, but a prominent example is the Facebook logo. It features a simple blue square with white lowercase letters spelling "f." Another example is the LinkedIn logo, which also uses a blue background and white lettering.
Blue square
The logo you're describing sounds like the logo for the company "Adobe." It features a dark blue square with a stylized white capital "A" inside it. This logo is often associated with Adobe's suite of creative software, including Photoshop and Illustrator, and represents innovation and creativity in digital design.
The logo you are referring to is likely the "In" logo of LinkedIn. It features the word "in" in white text, set against a blue square background. LinkedIn is a professional networking platform that connects users for career development and job opportunities.
"Nationwide insurance has a very basic logo. It is a white square with a blue thin border around the white square, with the word nationwide in white at the bottom of the blue square."
It's Axa
The company logo with a blue square and white G is for Gap. Gap is an American retail company founded in 1969.
The camera company Minolta has a blue circle with white lines.
axa
Hellmanns
Billabong
Blue square
Ryanair (british air line company).
The Tesco logo is one logo with a blue S and a red line underneath.
Blue Square North
The white cross on a red square is the swatch logo