Hello Suzanne.
I found some records that lead to your great grandfather was named after his grandfather.
He was the son of Robert Burns, born 22 Aug. 1853 in Clay Co., Kentucky.
Name: Robert Burns
Sex: Male
Birth Date: 22 Aug 1853
Birthplace: Clay, Kentucky, United States
Father's Name: Hugh Burns
Father's Sex: Male
Mother's Name: Eliza Collins
Mother's Sex: Female
Event Type: Birth
Reference: Item 1
Digital Folder Number: 005552463
Microfilm Number: 216821
Originating System: ODM
Indexing Batch: C51724-1
Citing this Record
"Kentucky Births and Christenings, 1839-1960", database, FamilySearch (https://familysearch.org/ark:/61903/1:1:FWK4-HZP : 22 July 2021), Robert Burns, 1853.
Robert Burns married Sarah Jane Boggs 30 Jan 1879 in Calhoun, West Virginia.
Name: Robert Burn
Event Type: Marriage
Age: 25 years
Marital Status: Single
Birth Year (Estimated): 1854
Birthplace: Clay County, Ky
Marriage Date: 30 Jan 1879
Marriage Place: Calhoun, West Virginia
Father's Name: Hugh Burn
Mother's Name: ...
Spouse's Name: Sarah Jane Boggs
Spouse's Age: 21 years
Spouse's Marital Status: Single
Spouse's Birth Year (Estimated): 1858
Spouse's Birthplace: ...
Source Reference: County Records
Record Number: 86
Reference ID: v 1 p 60
GS Film Number: 807456
Digital Folder Number: 004011510
Image Number: 65
Indexing Project (Batch) Number: M73683-3
Citing this Record
"West Virginia Marriages, 1780-1970," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:FRDL-SJQ : 16 March 2020), Robert Burn and Sarah Jane Boggs, 30 Jan 1879; citing Calhoun, West Virginia, v 1 p 60, county clerks, West Virginia; FHL microfilm 807,456.
"United States Census, 1880," database with images, FamilySearch (https://familysearch.org/ark:/61903/3:1:33SQ-GYBD-96PR?cc=1417683&wc=XH13-4WL%3A1589415848%2C1589394842%2C1589395058%2C1589395189 : 24 December 2015), West Virginia > Calhoun > Lee > ED 142 > image 4 of 6; citing NARA microfilm publication T9, (National Archives and Records Administration, Washington, D.C., n.d.)
Robert Burns and his wife Sarah are listed at the top of the Census sheet cited above. The Census was taken in 15 Jun 1880. There also is listed their firsborn, your great grandfather Hugh, he was born November 1879 (a +/- 1 year error in dates of birth is very usual).
Many records on your great grandfather Hugh Burns state he was born in Kentucky instead of West Virginia, but I found the certificate of death of his daughter Gertrude (3 yrs. 6 mos. 14 days). He is listed as the informant and he said he was born in West Virginia. See the document:
"Kentucky Death Records, 1911-1967," database, FamilySearch (https://familysearch.org/ark:/61903/3:1:S3HY-67PY-NK?cc=1417491 : 3 January 2019), > image 1 of 1; Office of Vital Statistics, Frankfort.
His daughter Gertrude was named after his sister. His sister Gertrude married 5 Mar 1914 (she remarried later), according to the record she was born 3 Oct. 1894 in Oneta, Kentucky:
Name: Peter A Paggioli
Sex: Male
Age: 25
Residence Place: Louisville, , Kentucky
Birth Date: 22 Apr 1889
Birthplace: , , New York
Race: White
Number of Previous Marriages: 1
Father's Name: Louis Paggioli
Father's Sex: Male
Mother's Name: Dor Ningukon
Mother's Sex: Female
Spouse's Name: Gertrude R Burns
Spouse's Sex: Female
Spouse's Age: 20
Spouse's Residence Place: , , New York
Spouse's Birth Date: 03 Oct 1894
Spouse's Birthplace: Oneta, , Kentucky
Spouse's Race: White
Spouse's Previous Marriage Number: 1
Spouse's Father's Name: Robert Burns
Spouse's Father's Sex: Male
Spouse's Mother's Name: Sarah Boggs
Officiator's Name: Oscar L Hoy
Marriage Place: Clark, Indiana
Marriage License Date: 05 Mar 1914
Marriage License Place: Clark, Indiana, United States
Event Type: Marriage License
Record Number: 231
Page: 509
Number of Images: 1
Digital Folder Number: 004476680
Microfilm Number: 001415921
Image Number: 00786
Indexing Batch: M02970-5
Citing this Record
"Indiana Marriages, 1811-2019," database with images, FamilySearch (https://www.familysearch.org/ark:/61903/1:1:XXGB-LSN : 3 August 2022), Peter A Paggioli and Gertrude R Burns, 05 Mar 1914; citing Clark, Indiana, United States, Marriage License, Indiana Commission on Public Records, Indianapolis; FHL microfilm 004476680.
Gertrude died 1 Jan 1981. There is (again) the +/- 1 year mistake in her date of birth in this record.
Name: Gertrude Burns
Sex: Female
Age: 85
Death Date: 01 Jan 1981
Death Place: Bristol, , Virginia, United States
Birth Date: 03 Oct 1895
Race: White
Father's Name: Robert Burns
Mother's Name: Sarah J Boggs
Spouse's Name: Scott Burns
Spouse's Sex: Male
Event Type: Death
Registration Date: 27 Jan 1981
Military Status: No
Registration District Number: 201
Digital Folder Number: 100937152
Image Number: 00367
Citing this Record
"Virginia, Death Certificates, 1912-1987," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:QVBV-FBMM : 16 August 2019), Gertrude Burns, 01 Jan 1981; from "Virginia, Marriage Records, 1700-1850," database and images, Ancestry (http://www.ancestry.com : 2012); citing Bristol, , Virginia, United States, entry #, Virginia Department of Health, Richmond.
Please, see the original documents in the records, you may find some more information.