Others have commented about their approach to record entry.
Luke also asked, "Is there a standard convention?"
A good way of familiarizing yourself with standard practices is to read scholarly journals; examples from the United States are The Register, The Quarterly and The Record.
For the purpose of your question, I happened to pull a copy of The Register, v161 (January 2007). Skimming the issue quickly, I found two articles that remarked about unnamed children. In both cases, the given name space was simply "child"; references follow.
Deborah Kimball Nowers, "Osmond Trask and his children of Salem and Beverly, Massachusetts," The New England Historical and Genealogical Register 161 (Jan 2007): 47-61, p. 59 for the two children, numbered and listed as:
ix. Child, d. 18 Jan 1730-31.
x. Child, d. 7 April 1731.
Both the above entries cite the Vital Records of Beverly; 2:580 and 2:583, respectively.
Register-style Child Lists, from which the entries above were extracted, omit the surname; so generally the given name only appears.
This example is perhaps more interesting, given the lifespan information.
R. Andrew Pierce, "Joseph Daggett of Martha's Vineyard, his Native American wife, and their descendants," The New England Historical and Genealogical Register 161: 5-21, see p. 19 for the Child List entry:
ii. child, b. by Oct. 1725; d. before 17 July 1747, the date of Edward Cottle's deed described above.
From the description, the existence of the child seems inferred from the will; I didn't further research.