You can use R and Bioconductor's GenomicRanges package as follows:

First, represent your regions of interest as genomic ranges. For real data, you may load a BED file with the function rtracklayer::import.bed(). Here, we create by hand the three regions that you gave as example. The output of the commands is displayed in italics.

# In R, load the library.
library(GenomicRanges)

# Create an GRanges object (here called, 'r'). that contains the regions of interest.
r <- c( GRanges("chr1", IRanges(1013574,1013576))
      , GRanges("chr1", IRanges(1013984,1014478))
      , GRanges("chr1", IRanges(1020163,1020383)))
r

Output:

GRanges object with 3 ranges and 0 metadata columns:
      seqnames             ranges strand
         <Rle>          <IRanges>  <Rle>
  [1]     chr1 [1013574, 1013576]      *
  [2]     chr1 [1013984, 1014478]      *
  [3]     chr1 [1020163, 1020383]      *
  -------
  seqinfo: 1 sequence from an unspecified genome; no seqlengths

Then, load genomic ranges for an annotation, for instance GENCODE.

# Get GENCODE from the Bioconductor's Annotation Hub.
library(AnnotationHub)
ah <- AnnotationHub()
query(ah, c("Gencode", "gff", "human"))

Output:

AnnotationHub with 9 records
# snapshotDate(): 2016-12-29
# $dataprovider: Gencode
# $species: Homo sapiens
# $rdataclass: GRanges
# additional mcols(): taxonomyid, genome, description, tags,
#   sourceurl, sourcetype 
# retrieve records with, e.g., 'object[["AH49554"]]' 

            title                                                    
  AH49554 | gencode.v23.2wayconspseudos.gff3.gz                      
  AH49555 | gencode.v23.annotation.gff3.gz                           
  AH49556 | gencode.v23.basic.annotation.gff3.gz                     
  AH49557 | gencode.v23.chr_patch_hapl_scaff.annotation.gff3.gz      
  AH49558 | gencode.v23.chr_patch_hapl_scaff.basic.annotation.gff3.gz
  AH49559 | gencode.v23.long_noncoding_RNAs.gff3.gz                  
  AH49560 | gencode.v23.polyAs.gff3.gz                               
  AH49561 | gencode.v23.primary_assembly.annotation.gff3.gz          
  AH49562 | gencode.v23.tRNAs.gff3.gz

The command above returned that the ID for GENCODE 23 is AH49556 and indicated which command to run next.

ah["AH49556"]
gc <- ah[["AH49556"]]

Then, intersect your regions of interest with the annotation.

overlaps <- findOverlaps(r, gc)

This returns an object telling which region overlaps with which annotation. The last step is to extract the gene names, collate them, and prepare your final output.

genes <- extractList(gc$gene_name, as(overlaps, "List"))
genes <- unstrsplit(unique(genes), ";") # Needed in case more than one gene overlaps.
paste(as.character(r), genes)

[1] "chr1:1013574-1013576 ISG15" "chr1:1013984-1014478 ISG15"
[3] "chr1:1020163-1020383 AGRN"

You can find other examples on how to use findOverlaps() in other Biostars posts or in Bioconductor's support forum.

Maybe you could try bedtools. First, go to ensembl and download refgenome's gtf file. Then use 'bedtools intersect -wo -a ref.gtf -b you_input.bed"