I'm not sure what you mean by 'special name', but the official name for the British flag is: Union Jack
The term "Union Jack" is not considered correct because a Jack is a flag flown from a ship and British merchant ships fly the Red ensign and the Royal Navy flies the White Ensign. The Official title of the Flag of the United Kingdom is the "Union Flag" and unoffically "British Flag" although this term might be considered controversial in Northern Ireland
The U.k
Scotland
Union Flag, or more casually the Union Jack
The Union Jack is the nickname of the UK flag.
New Zealand is a commonwealth country which derived from English origins thus the Union Jack.
The same flag that it flies at other times - the Union Flag - sometimes incorrectly called the Union Jack.
The jack refers to the jackstay of a ship, on which the Union Jack would be displayed. Strictly speaking the flag should be called the Union Flag, but Union Jack is well known. Actually, the union jack is what the flag is called out at sea, but the union flag is what they call it on land.
Because Samoa is an independent country, not a British colony.
because before Australia became a republic (independent country) it was ruled by England. Australia still has strong ties with england, so the union jack is on the flag to show this relationship.
The jack staff on a Navy vessel is essentially a flag pole on the bow of vessel. Unlike the National Ensign (country flag) which flies on the stern flag staff of most ships (on the bridge while underway surfaced on a submarine), the jack staff flies a flag literally called a Jack. Over the years of Navy history, there have been many Navy Jacks flown from the Jack Staff; the current Jack ("Don't Tread On Me" flag) was ordered flown after the 9/11 attacks, replacing the traditional Jack, which was the field of blue with 50 stars (modern), or in years past, a field of blue with stars for every state in the Union. It is this flag from which the term "Union Jack" comes from.