(Spoiler: it's probably Fishel.)
In general, the easiest way to find the name of a person's parents is to look for records which might include those names, specifically death, marriage, and birth records.
You haven't given enough detail to be totally sure I found the right person, but I'll walk through my process so you can modify it if I found the wrong person, and understand it for future research.
A quick search for the name Jacob David Keil on either FamilySearch.org (free account required - see https://www.familysearch.org/ark:/61903/1:1:KFW5-RZ3 for this record) or Ancestry.com (costs money) turns up a death record for Jacob David Keil who died 27 July 1921 in Detroit, Michigan, USA, and was 67 years old (making birth year approximately 1854). FamilySearch has his father's name indexed as "Tischel Keil", and Ancestry has it indexed as "Fischel Keil". Ancestry has a scan of the death certificate, which further includes the information that he was married to "Lottie Kale", lived at 1063 Delmar St, Ward 5, had been a resident of Detroit for 4 years, was a tailor working for himself, and his father's name looks like "Fischel Keil" to me. Note that the mother's name is listed as "Unk", meaning unknown by the informant, who was his wife. His burial place is "Machpalah" cemetery.
(https://www.kveller.com/jewish-baby-name/fishel/ says that Fishel is a Yiddish name meaning little fish, though I would be remiss if I didn't mention that the definitive source for such information is the book "A Dictionary of Ashkenazic Given Names" https://www.avotaynu.com/books/dagn.htm)
It is common practice for Jewish tombstones (in the US and many other places) to include the person's Hebrew name, which lists their given name(s) and their father's given name(s). Searching FindAGrave.com for Jacob Keil with death year 1921 finds https://www.findagrave.com/memorial/51936122/jacob-david-keil which is at Machpelah Cemetery in Ferndale, Michigan, near Detroit.
Searching FindAGrave for all people named Keil buried at that cemetery finds https://www.findagrave.com/memorial/51936125/lottie-keil for Lottie Keil, with a photograph showing the stone says she died 7 July 1930, aged 70 (meaning she was born around 1860, matching what you said). You didn't ask it, but her Hebrew name is Zlote Leah, daughter of Mordechai Zvi (apologies for my probably nonstandard transliteration of the Hebrew). It makes sense that she went by Lottie in the US, since it sounds a lot like Zlote.
The cemetery has a web site https://www.machpelahcemetery.org/ and on that page you can find the "Burial List K" link which goes to https://www.machpelahcemetery.org/burial-list/burial-list-k/ and then search for Keil. That returns the records for Jacob David Keil and Lottie Keil (as well as three other people with this surname, who might be related). Jacob's grave is listed as grave 663, section C, row 03, lot 27.
If all this matches the information you know, the next step I would take if it were my research is to get a picture of Jacob David Keil's grave. If you live nearby, you could go there yourself, after having called them to get directions to find it. If you're not nearby, you can go to the FindAGrave page and click "Request Photo", and enter your request and then hope that a volunteer goes to the cemetery and takes a picture of the grave (there are only 4 open photo requests in this cemetery, all opened in the last month, so there's a decent chance someone might get to it quickly).
This answer is already very long, so I'll just mention that if the records in the US didn't answer your question, then you would need to expand your search, likely to records from his place of birth, starting on JewishGen (jewishgen.org) or Gesher Galicia (https://search.geshergalicia.org/); or research his known siblings and other relatives, if any, in the hope of finding information that led to his father's name. You didn't ask about his mother's name, but to find her name you might well have to find records from Europe.