The afterword to volume 1 briefly describes the conception of the series. It explains that the setting of a concept cafe came first. Then the content of the series was decided in parallel to the characters. "Alter ego" is translated from uraomote (裏表), which is literally back+front. The fact that the cafe itself is divided into a front of house and staff only areas at the back is an example of what this can refer to, in relation to a physical place. The way the serving staff play roles when they're in the front of house, contrasting with how they are off-duty is another example.
But used in relation to people uraomote has a broader meaning—the concept of people having private, interior, hidden sides and public, exterior, visible sides. This is a fairly common theme in Japanese stories, interested in the gap between public and private, and also the intimacy involved in exposing your true thoughts and feelings. It's easy to see instances of how it is explored in the characterization in this series. Hime's cute facade is her exterior and her aim to be loved by everyone and marry for money is her interior. Kanoko's hidden side is her stalker behavior and romantic feelings toward Hime. Mitsuki struggles to process people having an interior different to what's on display. Sumika being a keen reader is hidden behind her gal exterior. And so on.
The concept cafe has a yuri theming. It's a setting where it would have been quite natural to have conversations about the yuri genre between yuri fans as characters, but WataYuri generally avoids doing that. In 13+ volumes there have been remarkably few occasions where a character talks about yuri and when they do it seems to serve as a bit of characterization or to explain the premise of the cafe. The main characters mostly display little interest in the yuri genre. But the clientele being yuri fans does mean that they are depicted as being there for the interaction between the servers, whereas in a maid cafe, the standard kind of concept cafe, the work is largely about charming the customers by how the server acts toward the customer.
Specifically the cafe is based on Maiden's Heart, a fictional series which is introduced as basically a legally distinct riff on Maria-sama ga Miteru, including tie straightening and it being influential on yuri. Maiden's Heart was apparently set in Germany, so instead of sœurs there are schwestern, but they work the same, e.g. the relationship is symbolized by the exchange of a cross, which is an invention of MariMite. MariMite is a natural thing to draw on for the basis of a yuri concept cafe. With MariMite you can identifiably reference it and yet have it come across like it's stereotypical yuri iconography, bringing to mind all yuri set in posh girls' schools, despite WataYuri not recognizably referencing anything other than MariMite. Other details about Maiden's Heart are freely invented to suit WataYuri.
I think the sœur/schwester concept taken from MariMite is useful because it reads clearly as yuri entertainment for the cafe customers since the relationship between schwestern is less private than lovers, but also less physical so there's less of an issue around what staff could be asked to do by a cafe (especially as most of them are minors). On top of that, the concept of having to pretend to be schwestern gives an impetus for the drama with Hime and Mitsuki at the beginning. It's the common device of a story having some kind of circumstance that puts 2 characters together.