[kszx]

His father also called him Loong (not Hsien Loong), at least sometimes:

"He was still young and it was better that someone else succeed me as prime minister. Then, were Loong to make the grade later, it would be clear that he made it on his own merit."

http://www.singapore-window.org/sw04/040531a1.htm

(They use English in the family, although Lee Hsien Loong can speak Chinese fairly well.)

[kzrdude]

His father called him by his first name, that sounds expected.

[hboon]

Hsien Loong is his first name. Chinese usually don't have middle names. Calling him "Loong" is the equivalent of calling Tommy Tom. But it's more intimate, usually only used by someone closer to the person.

[yen223]

His brother is Lee Hsien Yang, so his father probably calls him Loong to distinguish him from the brother.