The codes and instructions for annotating gene names to the result table for differential gene expression analysis in DESeq2 seem to be for using Ensembl as the reference genome in the alignment step. I'm wondering if there are instructions/codes for annotating gene names if I used UCSC hg19 as the reference genome in the alignment step? Thanks for your help.

Are you referring to the workflow? 

You can choose from any of the keys and columns of the annotation database package, for example:

columns(org.Hs.eg.db)

##  [1] "ENTREZID"     "PFAM"         "IPI"          "PROSITE"      "ACCNUM"       "ALIAS"      
##  [7] "CHR"          "CHRLOC"       "CHRLOCEND"    "ENZYME"       "MAP"          "PATH"       
## [13] "PMID"         "REFSEQ"       "SYMBOL"       "UNIGENE"      "ENSEMBL"      "ENSEMBLPROT"
## [19] "ENSEMBLTRANS" "GENENAME"     "UNIPROT"      "GO"           "EVIDENCE"     "ONTOLOGY"   
## [25] "GOALL"        "EVIDENCEALL"  "ONTOLOGYALL"  "OMIM"         "UCSCKG"

Here in the org.Hs.eg.db package we have UCSC known gene (UCSCKG), etc. For more information on any of these ?UCSCKG.

See AnnotationDbi for more information on how to use the annotation database packages.