You'll need to join to another instance of the person table. You can do this in SQL by using a table alias in your JOIN clause.
SELECT dt.declare_time,
p.first_name,
p.last_name,
dt.amount,
dt.last_modified_time,
dt.Last_Modified_User_ID,
dtp.first_name,
dtp.last_name
FROM declared_tip dt
JOIN person p ON dt.person_id = p.id
JOIN person dtp ON dt.Last_Modified_User_ID = dtp.id
Note the "dtp" fields at the end of the SELECT. If you want to concatenate them, you can, but this will show them as separate fields.