Onomastics should not replace the surnames tag, as there is not a one-to-one correspondence between the two terms.
One can certainly find instances where onomastics and genealogy go hand in hand. A quick Google Search turned up one such example:
Dictionary of Americanized French-Canadian Names: Onomastics and
Genealogy July 2018 Names: A Journal of Onomastics 66(3):196-198
DOI:10.1080/00277738.2018.1500988
However, when I search on JSTOR for the terms "onomastics" and "genealogy", I get 353 results; when I search for "surnames" and "genealogy", I get 14,292 results. (Note that some of the articles containing "genealogy" are not using it as a term for family history.) "Onomastics" plus "surnames" yields 1,067 results.
Onomastics is the term for the study of proper names, yes, but a proper name can consist of multiple components, as this excerpt from the Stanford Encyclopedia of Philosophy shows:
The Cambridge Grammar of English distinguishes the syntactic category
of proper name from that of proper noun (Payne & Huddleston 2002:
516). A proper noun is a word-level unit of the category noun, while a
proper name is a type of noun phrase. So, for example, the proper name
“Alice Walker” consists of two proper nouns: “Alice” and “Walker”. A
proper name (the noun phrase) may also—and often does—consist of a
single proper noun, just as a verb phrase may consist of a lone verb.
A surname is a subset of the kind of name one might study for genealogy.
The volume on all our tags is low, and it may not seem to matter if we choose one term over another. However, what happens in the future if the activity on the site is at a much bigger scale?
Stack Overflow's What are tags, and how should I use them? says:
"Tags can also be used to help you identify questions that are interesting or relevant to you."
Removing or replacing surnames as a tag means that people who are primarily interested in surname studies can't follow questions about surname studies, an important part of Genealogy and Family History. They won't be able to separate questions about surnames from questions about naming patterns (which might also involve the use of given names) and other questions about name variations.
What makes onomastics a good fit for our site?
As for the two questions recently tagged onomastics, and any other name questions that might come up on the site: I would like to see some indication of why the question was posted here and not on Linguistics SE.
Compare and contrast with DNA questions. Questions about genetic genealogy are a good fit for Genealogy SE. Questions about DNA topics that do not have a bearing on genetic genealogy are better suited to the more science-related Stack Exchange sites where they are more likely to be seen by experts who can answer them.
In other words, if you are tracking the descendency pattern of genes (like BRCA) that predispose you to a particular medical condition, and you want to know how to record causes of death in your software,or make a chart showing who had the disease to show your family, etc. that is a Genealogy SE question. If you are asking about the science behind the test to detect for the presence of BRCA, or other science-based issues (eye and hair color, etc.), ask on the science sites. See the previous discussion at genealogy.meta.stackexchange.com/a/1426/6485.
