Below are assumed from the question:

1. response.data is an Array
2. Each element in this Array is an object
3. Each such object has a prop named teamMember
4. Each teamMember has a prop named customFields which is an Array
5. Each element of the Array (at point 4 above) has a prop name

The objective is to filter only those elments from customFields array where the element's name prop matches the value ByLine.

One possible way to achieve this:

const getIndexOfByLine = (arr = item.teamMember.customFields, matchNameWith = 'ByLine') => (
  arr
    .map((el, i) => ({elt: el, idx: i}))
    .filter(obj => obj.name === matchNameWith)
    .map(obj => obj.idx)
    [0]
);

NOTE: If more than 1 element has name as 'ByLine' then only the first index is returned.

Explanation

• Iterate through the item.teamMember.customFields array using map with element as el and index as i.
• For each element in the array, return an object with two props namelyelt and idx

.map((el, i) => ({elt: el, idx: i}))

• In the resulting array, apply the filter and keep only those elements where name matches ByLine (can be changed via parameter matchNameWith)

.filter(obj => obj.name === matchNameWith)

• Now, we have an array with objects that have the two props elt and idx. Since we only require the index, map the array to get only the index.

.map(obj => obj.idx)

• In case there were more than 1 elements that had 'ByLine' as the name, simply use the first occurance.

[0]

I used this and it worked

let byline=item.teamMember.customFields.filter(checkbyline);


function checkbyline(fields) {
  if (fields.name == 'Byline') {
  return fields.value}
else {return }
}   

and to use it on the HTML output

byline[0].value