Just to clarify, Minnie Goode and Rhoda Goode are the same person.

Birth certificate confirms that Rachel Goode is the mother of Minnie Goode. Elizabeth Goode reported the birth. Her mark is in the certificate.

Name: Minnie Goode
Year of Registration: 1869
Quarter of Registration: Apr-May-Jun
District: Westbury On Severn
County: Gloucestershire
Volume: 6a
Page: 222

The Name Rhoda is not on her birth certificate at all. Her name is Minnie Goode. Rhoda was added in at her baptism:

Year: 1869 Month: Nov Day: 7

Parents_Surname: GOODE
Child_Forenames: Rhoda Minnie

Fathers_Forenames: [not stated]

Mothers_Forenames: Rachel
Mothers_Surname:

Residence: Micheldean [sic]
Occupation: In Service
Officiating_Minister: William Charles Fox Curate
Event: Baptism
Memoranda:
Notes: Register_
Reference: P220 IN 1/4 Page_
Number: 38 Parish_Chapel: Mitcheldean