variable and database table(s?) names
We are clear on the fact that names should be in the plural. As for table(s) I think it should be singular before names (database table names) but plural if you choose to say names OF tables (this second phrasing is not idiomatic).
In database table names, "table" is an attributive noun which should normally be in the singular. On the site of the American Journal Experts I found this explanation which backs up what I have just said:
Two common pet peeves among language editors relate to incorrect noun pluralization, most often meaning that “s” or “es” is unnecessarily added to the end of a noun. The first type of error is unnecessary pluralization of a noun used as an adjective, also known as an attributive noun. For example,
- Nanoparticle structures (correct)
- Nanoparticles structures (incorrect)
- Five-week-old mice (correct)
- Five-weeks-old mice (incorrect)
Generally, an attributive noun should not be plural, even if the noun that is being modified (“structures” and “mice” in the examples above) is plural; exceptions to this rule (e.g., “sports games”) are infrequent.
Now, while searching for the phrasing you are giving I found this article on the teamten.com site, whose title is
Use singular nouns for database table names
The first sentence of the article has the other way of phrasing:
A common debate in relational database circles is whether the names of tables should be singular or plural.
If you look up these phrases on Gngram you will find that database table names is the one commonly used:

Note that
- names of database tables is almost not used.
- There is no instance of database tables names.