Two ways with subtly different results. "GROUP BY X" is another way of saying "Give me one row per X". You will have to apply an aggregation function to each other row so it knows how to squash the rows into 1:
SELECT MAX(Id),
       MAX(ConflictCheckRequestIndividualId),
       Name,
       MAX(Surname),
       MAX(it.IndividualType) AS IndividualType,
       MAX(JobTitle),
       MAX(RegistrationNumber),
       MAX(Title),
       MAX(District),
       MAX(Status),
       MAX(CreatedBy),
       MAX(Created),
       MAX(ModifiedBy),
       MAX(Modified)
  FROM ConflictCheckItoIndividual
  LEFT JOIN @IndividualTypes it
    ON it.IndividualId = ConflictCheckRequestIndividualId
 WHERE ConflictCheckRequestIndividualId IN
       (SELECT Id
          FROM ConflictCheckRequestIndividual
         WHERE ConflictCheckRequestId = @ConflictId
           AND SubStatus = 2)
GROUP BY Name
This might end up with data for each field coming from different rows. If you wanted all data to come from one row, you could do this
;WITH cte AS
(
SELECT Id,
       ConflictCheckRequestIndividualId,
       Name,
       Surname,
       it.IndividualType AS IndividualType,
       JobTitle,
       RegistrationNumber,
       Title,
       District,
       Status,
       CreatedBy,
       Created,
       ModifiedBy,
       Modified,
       ROW_NUMBER() OVER (PARTITION BY Name ORDER BY Modified DESC) as rownum
  FROM ConflictCheckItoIndividual
  LEFT JOIN @IndividualTypes it
    ON it.IndividualId = ConflictCheckRequestIndividualId
 WHERE ConflictCheckRequestIndividualId IN
       (SELECT Id
          FROM ConflictCheckRequestIndividual
         WHERE ConflictCheckRequestId = @ConflictId
           AND SubStatus = 2)
)
SELECT * FROM cte WHERE rownum = 1
This is "Partitioning" the data into one bucket per Name. Within each bucket, its ordering the rows by Modified in descending order. We then only pick out one row from each bucket - the most recently Modified one.
As an aside, given that there is a Name and a Surname field, I would expect to group by that as well