The tombstone seems to indicate his birth death and name. However, there also seems to be a Barton P. Hamm. Lots of people are combining them. I am wondering if I am wrong not to. Is Burton R's middle name Richard? I see Richard Hamm and Barton P. Hamm separate on the 1860 Census. Year: 1860; Census Place: Van Buren, Monroe, Indiana; Roll: M653_282; Page: 608; Family History Library Film: 803282
Year: 1860; Census Place: Beech Creek, Greene, Indiana; Roll: M653_262; Page: 637; Family History Library Film: 803262
I also see a federal tombstone request for Barton P. Ham stating he died 9 Nov 1878 https://familysearch.org/ark:/61903/1:1:V6H7-J3S
I also had to modify the birth and death of his "brothers" Lawson and Henry because they were identical to each other. This family seems to have many inconsistencies.
Interesting question. I had a look and found the marriage record of a Barton R. Haus to Sarah A Cooper
https://www.familysearch.org/ark:/61903/1:1:4FCF-N73Z?from=lynx1UIV8&treeref=L2YM-XVQ
And then this marriage record for child Harvey shows his parents as Richard Hamm and Sarah Cooper
https://familysearch.org/ark:/61903/1:1:D8TF-ZJPZ
I can see Barton R Haus using his middle name but to go from Haus to Hamm as a Surname is what I would question. Could be a transcription or spelling error on the marriage record. That record on FS has no digital image to look at. I would recommend you order the marriage registration or find a way to view the record so you can clear that question up. I don't see any indication from the attached parents that they went by Haus?
This family tree on FS https://www.familysearch.org/tree/person/sources/L2YM-XVQ
shows that Barton P Ham b. 1825 and Burton R. Hamm b. 1829, were brothers. I see he is attached as brother to Burton on Wikitree as well. Recommend you follow up on that. I don't think you should combine them as they appear in 1860 in separate locations and are married to different women.
There is also a marriage record for Barton P Ham to a Rebecca Rader
http://familysearch.org/ark:/61903/1:1:87RV-7FN2
Barton P Ham appears in the 1860 Census here, so not the same person as Burton R Hamm
https://familysearch.org/ark:/61903/1:1:M4NR-G26
Thanks for your help Lorraine. I just found Barton and Burton side by side with their mother so that is a big help.
"United States Census, 1850," database with images, FamilySearch (https://www.familysearch.org/ark:/61903/1:1:MHJF-MT2 : 12 February 2022), Boston R Ham in household of Anne N Ham, Beech Creek Township, Greene, Indiana, United States; citing family , NARA microfilm publication (Washington, D.C.: National Archives and Records Administration, n.d.).