I know this topic can be charged. But I disagree that it matters to have specific half-elves and half-orcs as unique rules objects that are called out.
I am a person that wants more diverse mixed-heritage options, but does not like the idea of a 3rd-party voice/narrator/writer grouping mixed-heritage peoples into "half"-anything. That's the only problem. They are whole individuals who as a character, individually choose if they want to identify as "half"-something, or utilize some other descriptor that is natural to their personal culture or sensibilities.
If there was a rules object called a "Half-orc" what does that even mean to a new player? Half-what? Can the other half of a half-orc be tiefling? If so, do they use the half-orc rules? Of course not. That naming convention doesn't work in a paradigm of dozens of mixed-orc possibilities. It is also untenable to invent new names for mixed races in the PH, not only because there are hundreds of pairings to have to invent, but also those naming conventions are not multiversal, rather are individually campaign-specific. We should not call all elf/dwarf hybrids "Dwelfs" or all elf/human hybrids "Khoravar" because those should be campaign-specific if the table wants to do that.
The baseline naming convention should be campaign-neutral and be able to convey any species combination. I'm thinking a descriptor like "Mixed" and the use of the two most prevalent species heritages that the character embodies. Some of the below descriptor options are better than others (I don't like Hybrid, to be honest), but I'll use some combos to show examples in use:
- Mixed Human/Orc
- Dwarf/Elf Descendant
- Tiefling/Aasimar Hybrid (hybrid sounds like a scientific design choice)
- Triton/Simic Hybrid Hybrid (nahhh)
- Dragonborn/Goliath Bloodlines
- Elf/Kender Parentage (but not all parents are blood)