I wonder if many would instinctively know to pronounce Ξ as "e".

I didn't if that's any indicator.

To get the desired result, I'd harness the natural propensity for the average human to discover through error.
Place the Ξ where most people would expect an E. The auto correction of the brain will likely correct it to E and then Ξ becomes associated with E while still remaining Ξ

Then they consciously notice that the E is a little funny and realize it is actually Ξ, bringing attention to the Ξ logo to Cement it being pronounced E as well as being used for the function of the letter it resembles.

It's not required for this suggester to be in incorporated into the name, and consequently constraining its form.
It Just has to be prominent on the website by replacing the Es of key words with Ξ

example:

Ξmail

Ξcosystem

Ξconomy

Ξcommerce

Ξfficiency

Ξlegance

Ξducation

Ξarth

Ξgress - Definition, the act or an instance of going, especially from an enclosed place.