This example shows you how to utilize jq to loop bash script through an array of JSON values.

loop-json.sh

jsonData='[{"name": "name#1","value": "value#1"},{"name": "name#2","value": "value#2"}]'
for row in $(echo "${jsonData}" | jq -r '.[] | @base64'); do
    _jq() {
     echo "${row}" | base64 --decode | jq -r "${1}"
    }
    
    # OPTIONAL
    # Set each property of the row to a variable
    name=$(_jq '.name')
    value=$(_jq '.value')

    # Utilize your variables
    echo "$name = $value"
done

# $ stoxe@box:~$ ./loop-json-test.sh 
#     name#1 = value#1\
#     name#2 = value#2

How bout just:

echo '[{"name": "name #1", "value": "value #1"} , {"name": "name#2", "value": "value#2"}]' |

   jq --raw-output 'map("\(.name) = \(.value)")[]'

name #1 = value #1
name#2 = value#2

---

Or if you really did want to drop down into the bash loop...
Could you avoid messing with base64 and multiple calls to jq and just use tabs to separate the values?

ie. where:

• jq outputs lines of tab separated values using @tsv
• then bash reads those lines into variables using $\t as the IFS (Input Field Separator)

echo '[{"name": "name #1", "value": "value #1"} , {"name": "name#2", "value": "value#2"}]' |

jq --raw-output 'map([.name, .value])[] | @tsv' |

while IFS=$'\t' read name value; do
    echo "$name = $value"
done

name #1 = value #1
name#2 = value#2

(NB. the sprinklings of whitespace in the input JSON for an extra degree of difficulty.)