I cannot but agree with the other commenters that this kind of problem does not look like it should ever be solved using SQL, but let us face it anyway.
SELECT CASE main.name WHERE preceding_id IS NULL THEN main.name ELSE null END, main.location FROM mytable main LEFT JOIN mytable preceding ON main.name = preceding.name AND MIN(preceding.id) < main.id GROUP BY main.id, main.name, main.location, preceding.name ORDER BY main.id
The GROUP BY clause is not responsible for the grouping job, at least not directly. In the first approximation, an outer join to the same table (LEFT JOIN below) can be used to determine on which row a particular value occurs for the first time. This is what we are after. This assumes that there are some unique id values that make it possible to arbitrarily order all the records. (The ORDER BY clause does NOT do this; it orders the output, not the input of the whole computation, but it is still necessary to make sure that the output is presented correctly, because the remaining SQL does not imply any particular order of processing.)
As you can see, there is still a GROUP BY clause in the SQL, but with a perhaps unexpected purpose. Its job is to "undo" a side effect of the LEFT JOIN, which is duplication of all main records that have many "preceding" ( = successfully joined) records.
This is quite normal with GROUP BY. The typical effect of a GROUP BY clause is a reduction of the number of records; and impossibility to query or test columns NOT listed in the GROUP BY clause, except through aggregate functions like COUNT, MIN, MAX, or SUM. This is because these columns really represent "groups of values" due to the GROUP BY, not just specific values.