Why did American labs use their own names while no lab outside of USA did that?

When an Eastmancolor films were printed in labs of Europe and other parts of the world, the name Eastmancolor was used.

But when it comes to American labs, they used their names instead

Eastmancolor films that were printed in Technicolor lab was called Technicolor despite that not all of them were printed in Technicolor Dye Transfer

Eastmancolor films that were printed in Deluxe lab was called Color by Deluxe

Eastmancolor films that were printed in Metro Gowden Mayer lab was called Metrocolor

Eastmancolor films that were printed in Warner Bross lab was called Warner Color

But outside of American labs, all was called Eastmancolor

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I actually did not share this anonymously. GAG did it by itself
Why did American labs use their own names while no lab outside of USA did that?
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