Surprisingly enough - two of Henry VIII's New Years Lists has survived to this present day! The first is from 1534 and the second is from 1539 - just five years between them but it made a huge different to Henry's personal life which can be seen in the receiving names on the lists.
The first list is Henry VIII's New Year List for who he was sending New Year-presents in 1534. But there is one person whose name is clearly missing from the list - Princess Mary or Lady Mary as she would be at that time. She still refused to accept her father's marriage to Anne Boleyn and thusly she is not included in her father's list - apparently he would not even send her a single present. The King's personal signature is clearly written as the very first name on the list and can also be found further down the scroll.
The second list is written by Henry VIII of the people to whom he would give New Year presents that year. The list is written around New Year's Day and is ranked from the most important to the least important. Some familiar names pop up when reading the scroll. At the top of the list was the "Lord Prince (Edward), the Lady Mariee (Mary) and the Lady Elizabeth" -
all three children were in the succession at the time. These three royal children are followed by a long list of bishops and after that the lords, duchesses and countesses.