Not weird but common. For Chinese family who uses 3 letter names, the boys will use the same second-letter in their name, the girls will use the same but different second-letter. Example Lee Hsien Loong and Lee Hsien Yang. So at home their parents probably call them Ah Loong or Ah Yang when they were kids. You can call him Loong if you're close to him or his senior relatives or his teachers. Chinese in south-east-asia still prevalently uses 3-letter name. But in China, more people have two-letter name.
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."
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.
They are from Singapore, not China. I have seen that such notions as last name, etc. are a bit distorted in immigrant communities, particularly for nth generation immigrants. A good example is first and last names of Indians in the Caribbean and South Africa, which are often distorted, weirdly spelled, etc.