Hybrids are fine, hybrids between genera are fine. Look at all the xGasteraloe hybrids in the database:
https://garden.org/plants/sear...
The problem is the second name attached to Alice's plant, beguinii. That is somebody's name (Beguin) turned into a Latin word, with a suffix added (-ius) and then made into the genitive (-ii). So it is Latinized, and therein lies the problem.
Botanists consider it a big deal whether a word is in Latin or not. Obviously since the days of Linnaeus, Latin has been a way of formalizing genus and species names (and so forth). There is a rule of botanical nomenclature (which I cannot locate for you right now) that says cultivar names should not ever be in Latin. I don't know how recent that rule is (like 20th century I guess), but the idea is there should be a firewall so when you look at the name of a plant, you know (or can usually guess) whether it is binomial nomenclature or not.
Now I don't know if these names predated the rule about Latin, maybe they get grandfathered in or something. But any plant with a Latin name (Noun adjective) that isn't described formally is a poseur, a wannabe, a pretender to the strict realm of scientific scrutiny. To the extent you can tell it has been Latinized, and to the extent you can tell if it has been published.
I do not mean to cast aspersion on anyone for the names they like to use. After all, in some sense all names are made up, and that is kind of the point. But there is this black and white rule.
You can look plants up in the Catalogue of Life to learn which Genus x species names are validly published. Only natural hybrids are represented in this group, as Zuzu has explained to me.
For example, a plant that is very near to my heart, Dudleya x semiteres. Here it is in the CoL and the database.
https://www.catalogueoflife.or...
Dudleya x semiteres
That is a natural hybrid found near here, between two native Dudleya species (the fancy word for it is nothospecies), and it was written up by Reid Moran in a formal way, at which time given the epithet "semiteres" which refers to the shape of the leaf. (Another story.)
xGasteraloe beguinii does not appear in the CoL, but other (presumably validly published) xGasteraloe names do.
Take another example.
There is a succulent Euphorbia hybrid called Euphorbia x japonica (or sometimes just E. japonica) and neither name is valid. There is no such species or natural hybrid (nothospecies) of succulent Euphorbia appearing in the literature, to the best of my knowledge. From a botanist's perspective, that is a "made up" name in the sense that it is not valid, it doesn't follow the rules. It is not even the only japonica, which makes it worse.
Somebody just came up with the name japonica and it caught on in the trade because the plant is incredibly easy to propagate, and everybody thought it was interesting that a succulent Euphorbia from a group found almost exclusively in South Africa would magically appear in Japan. Or whatever. I don't know the history. Not everyone is aware of this firewall.
So you will find Euphorbia japonica in the database by searching with those words, but you will be taken to this entry
Euphorbia 'Cocklebur'
because the name 'Cocklebur' is allowed. Even though almost every label I've ever seen on this plant says japonica.
So two things. There is the question of whether Latin can be used for a cultivar name. Not my call, it's officially frowned upon. And there is the question of whether Latinized names that have not been published the right way are acceptable, also not my call. ("Valid" is a word I have a hard time wrapping my head around, but I am not the one deciding it.)
I hope this long message clarifies instead of confuses things. Finally, and as a word of warning, you will find Latinized cultivar names all over the place in the database. There is no systemic correctness to it. But there seems to be more leeway for names like 'Variegata', in whatever common use sense. I'm not saying it's consistent, just explaining what its aspirations are (as I understand them).
