You could use biomaRt to get Refseq Transcript ID & Gene Symbol table:

library(biomaRt)
ensembl = useMart("ensembl", dataset="hsapiens_gene_ensembl")
results = getBM(attributes = c('refseq_mrna','hgnc_symbol'), mart = ensembl)

or if you have a list of Refseq Transcript IDs, say refseq_transcript_ID, then you can use:

results = getBM(attributes = c('refseq_mrna','hgnc_symbol'), filters = 'refseq_mrna', values = refseq_transcript_ID, mart = ensembl)

Alternatively, if you want a 'ready made' file with Transcript IDs and Gene Symbols, you can use gene2refseq.gz. The fields you are interested in are given under the names RNA_nucleotide_accession.version & Symbol.

And yes, Refseq Transcript ID to Gene Symbol is a many to one relationship.