Families did not always name a child right away. A search of the 1880 census at Ancestry.com for the first name of “Baby” and a birth year range of 1879-1880 resulted in 2927 results. Even if some of these are incorrect transcriptions, they are all not.
Search results for names in the 1880 census index at Ancestry.com with a birth year range of 1879-1880 had the following results:
Even if some of these were foundlings whose names weren’t truly known, it seems reasonable that not having an immediate name was not unheard of.
If you think your relative’s census enumeration is unusual, it’s advised to see if there were other similar enumerations in the census. That’s the same with any record.