Babies born on the same day will receive a limited edition silver coin, it was also announced yesterday.
The flurry of activity has included an unusual customer who walked into a betting shop and tried to place £100 on Mary at odds of 14/1.
"The mystery punter came into one of our shops in west London, in full Ascot fig with a top hat and tails. £100 is a huge bet for this market, where the average bet is just £3, so we are a little nervous that a member of the party at Royal Ascot has let the possible name slip," a spokesperson for William Hill said.
Rival Paddy Power has also seen a huge demand for the "novelty bets".
"Baby betting is booming with turnover expected to nudge £300k over the next week - a big increase on the royal wedding.
"The betting suggests we're in line for a princess with a 60/40 split in favour of a girl. Alexandra - the Queen's middle name - remains the hot favourite in the baby name game," a spokesperson said.
Meanwhile, Prime Minister John Key is tight-lipped on the gift New Zealand will send the royal couple when their child is born.
A spokesperson for Mr Key said when Prince William was born, New Zealand gave him a fine lace shawl, designed, spun and knitted by Margaret Stove.
Known as the bush bouquet shawl and featuring New Zealand plant patterns, the shawl was presented at Prince William's christening in 1982.
Former Australian prime minister Julia Gillard created a storm last month when she appeared in the Australian Women's Weekly knitting a toy kangaroo for the royal baby.
Antiseptic cream company Sudocrem has commissioned celebrity jewellery designer Theo Fennell to create a lavish baby gift, worth more than $19,000 - a jewel-encrusted, 18-carat white gold charm bracelet with an inbuilt nappy rash-cream holder.
The Finnish Government has given the couple a care package that includes condoms, leggings, hairbrush and nappy rash cream. Expectant mothers in Finland are given the same box.
- Telegraph, APNZ
