Does anyone know how I may be able to confirm the parents of an infant whose burial certificate has been transcribed?

I am the great grandson of Thomas Nash and Sarah Jane Cooksey, and I believe that my father may be named after an infant Thomas Henry Nash, died 1894 (record below). My great grandparents were not the only Nashes living in Ruspidge at that time.

Is there any way to determine the parents of this infant? There is no baptism record--likely, he passed away before being baptised. Thanks!

Thomas Henry NASH

Entry Number: 256
Year: 1894
Month: Feb
Day: 28
Surname: NASH
Forenames: Thomas Henry
Place of Residence: Ruspidge, Cinderford
Age at Death: 2 months
Officiating Minister: J. H. N. Barton, Curate
Cause of Death:
Memoranda:
Transcriber's Notes:
Register Reference: P85/1 IN 1/14
Page Number: 32
Church/Chapel: Cinderford