If we have two tables, people and groups, where people has a column group_ids which is an array of ids from groups, we can map the array of ids to the matching name from groups using the following query:

select
    p.email as email,
    coalesce(groups.names, '') as group_names

from people as p
    inner join (
        select string_agg(g.name, ', ') as names, person.id as person_id

        from entity_groups as g
            inner join (
                select id, unnest(group_ids) as group_id
                from people
            ) as person on person.group_id = g.id

        group by person.id
    ) as groups on groups.person_id = p.id

order by email;

It is a three-step process, listed inside to out (i.e. the innermost query is executed first):

1. Convert the group_ids array from people into a table of person_id and group_id using unnest
2. Join the group_id with the id of groups to get the name of the group
3. Aggregate the name of the groups into a comma-separated string using string_agg