They don't have aliases. Also, as Arcie did point out in forum #394322, Genshin Impact also has a character named Dahlia (Genshin Impact), so if anything such an alias would just be more confusing when both games which are popular in their own right (though Genshin much more so) are releasing characters with the same "name" at around the same time. That provides an even stronger justification to wait things out first before giving the alias. I can't even say "people will want to find the woman more" since Genshin Impact has a considerable number of its male characters that get posted and searched for regularly.
Speaking from my own point of view, all materials I've seen of Constance (and the Everflame Mansion altogether) more often used "Constance" than they did "Dahlia" so there's already considerable precedent. People tend to use a name more unless the codename or title are more common that it becomes synonymous with the character rather than an alternate form of address.
When all playable characters' names match their proper name then it becomes easy to leave that as the footnote, but whenever a character breaks convention as Constance (Honkai: Star Rail) now does, it's important to truly consider whether or not the alias is going to be properly worth it. This early on, we don't have enough information to make a proper conclusion about that. This definitely won't be the last time such a consideration has to be made either.
This is the same philosophy I approach Honkai Impact 3rd tag names and aliases with. For consistency the current expectation is to use full names without qualifiers until it's either ambiguous or a codename has more precedence than an actual name. This means that not all characters match their in-game names.