Here's LEFT JOIN variant of Anthony's answer (removes consecutive id's from the results)
SELECT a.*
FROM mytable a
LEFT JOIN mytable b ON a.Name = b.Name AND a.SectionID = b.SectionID + 1
WHERE b.SectionID IS NULL
EDIT: Since there is another interpretation of the question (simply getting results where id's are more than 1 number apart) here is another attempt at an answer:
WITH alternate AS (
SELECT sectionid,
name,
EXISTS(SELECT a.sectionid
FROM mytable b
WHERE a.name = b.name AND
(a.sectionid = b.sectionid-1 or a.sectionid = b.sectionid+1)) as has_neighbour,
row_number() OVER (PARTITION by a.name ORDER BY a.name, a.sectionid) as row_no
FROM mytable a
)
SELECT sectionid, name
FROM alternate
WHERE row_no % 2 = 1 OR NOT(has_neighbour)
ORDER BY name, sectionid;
gives:
sectionid | name
-----------+------
1 | Dan
4 | Dan
2 | Tom
7 | Tom
9 | Tom
Logic: if a record has neighbors with same name and id+/-1 then every odd row is taken, if it has no such neighbors then it gets the row regardless if it is even or odd.
As stated in the comment the condition is ambiguous - on start of each new sequence you might start with odd or even rows and the criteria will still be satisfied with different results (even with different number of results).