The USDA Plants Database gives as recognized synonyms for Rosa carolina L. var. carolina:
Rosa carolina L. var. deamii (Erlanson) Deam, Rosa carolina L. var. glandulosa (Crép.) Farw., Rosa carolina L. var. grandiflora (Baker) Rehder, Rosa carolina L. var. lyonii (Pursh) Palmer & Steyerm., Rosa carolina L. var. obovata (Raf.) Deam, Rosa carolina L. var. sabulosa Erlanson, Rosa carolina L. var. villosa (Best) Rehder, Rosa lyonii Pursh, Rosa palmeri Rydb., Rosa serrulata Raf., Rosa subserrulata Rydb. and Rosa texarkana Rydb.
Source: http://plants.usda.gov/core/profile?symbol=ROCAC

ITIS (Integrated Taxonomic Information System) gives the following accepted synonyms for Rosa carolina ssp. carolina L.: Rosa lyonii Pursh, Rosa serrulata Raf., Rosa carolina var. carolina L., Rosa carolina var. deamii (Erlanson) Deam, Rosa carolina var. sabulosa (Erlanson), Rosa carolina var. villosa (Best) Rehder, Rosa carolina var. glandulosa (Crép.) Farw., Rosa carolina var. grandiflora (Baker) Deam, Rosa carolina var. lyonii (Pursh) E.J. Palmer & Steyerm., Rosa pusilla Raf., Rosa petiolata Rydb., Rosa treleasei Rydb., Rosa aucuparia Rydb., Rosa caroliniana Michx., Rosa globosa Raf., Rosa humilis Marshall, Rosa lindleyi Spreng. and Rosa parviflora Ehrh.
http://www.itis.gov/servlet/SingleRpt/SingleRpt?search_topic=TSN&search_value=837335