But Kate, who is five months pregnant, said that the Duke, who attended the event with her, would prefer to have a girl.
Ahead of watching the parade at Mons Barracks in Aldershot, Hampshire, the Duchess suffered an embarrassing mishap when the heel of one of her shoes became stuck in a drain.
Kate, who showed patriotic spirit in the same green Emilia Wickstead dress coat she wore to the event last year, had to lean on William while she pulled it out with her hand.
Afterwards, the royal couple chatted to soldiers from the 1st Battalion Irish Guards in the Guardsmens' cookhouse.
Guardsman Lee Wheeler, 29, said: "I was talking to her about the baby, of course.
"I asked her 'do you know if it's a girl or boy', and she said 'not yet'.
"She said 'I'd like to have a boy and William would like a girl'. That's always the way.
"I asked her if she had any names yet and she said no.
"I said I suppose you've got to stick to traditional names."
Guardsman Jason Perry, 33, also spoke to Kate about her pregnancy.
He said: "I wished her congratulations and said I hoped everything is fine. She said 'yes it is'
"I asked her if she was excited to be having her first child. She said 'very'."
The soldier said it was "absolutely brilliant" to meet the couple and they had both asked him about his 13-and-a-half year career in the Army, which has seen him serve two tours of Iraq and one in Northern Ireland.
William, who wore the ceremonial dress of the Irish Guards, sipped on a glass of sherry inside the dining hall while the pregnant Duchess went without a drink.
The pair were loudly cheered by the soldiers as they entered the hall, which gave them welcome shelter from the heavy rain outside.
Before going inside, the Duke and Duchess had put on a brave face as they posed for formal photographs with officers and sergeants in the torrential rain.
The wet weather had earlier held off as the royal couple watched the parade take place under the cover of a podium.
Under grey skies, the Duchess took her position next to the Duke, who was attending the event as Colonel of the Regiment and for the first time wore an insignia aide de camp to the Queen on his shoulder, which was bestowed on him today.
The couple looked as about 200 soldiers paraded through the puddle-strewn square, bringing a splash of colour to the occasion in their full ceremonial uniform of scarlet tunics and bearskins, and led by the Band of the Irish Guards.
Kate, who had her hair up and wore an elegant black hat with a felt flower, finished off her outfit with black tights and heels.
The Duke watched as she presented traditional sprigs of shamrock to the officers and guardsmen, including one to himself.
Many of the soldiers who received the sprigs wore them in the front of their caps, as did the Duke, while Kate attached one to her lapel, next to a shamrock brooch.
The last sprig was given to the regiment's new mascot, seven-month-old Irish wolfhound Domhnall, who was carrying out his first public engagement.
Wearing a smart scarlet cape that matched the tunics of the soldiers, he was led over to Kate by his handler, Drummer David Steed.
The Duchess smiled as she bent down to attach the foliage to his silver collar.
The presentation of sprigs of shamrock by a senior female member of the royal family is a century-old tradition which was started by Queen Alexandra, the wife of Edward VII, in 1901.
The role was famously carried out by the Queen Mother.
The rain briefly stopped as William and Kate chatted to soldiers in the square after the parade.
The Duchess was given a posy of flowers by five-year-old Maisie Purcell, daughter of Company Sergeant Major Andy Purcell.
As she bent down to talk to Maisie and her friend Chloe Rigby, three, the Duchess told them: "Very nice to meet you."
After being handed the bunch of white and yellow flowers, she added: "Very spring-like."
Afterwards, a bashful Maisie said: "She said they look pretty."
Her mother, Suzy Purcell, 32, said: "She just came over and asked if they'd seen the dog and if we were cold."
Company Sgt Maj Purcell said the Irish Guards' St Patrick's Day celebrations were a "long tradition".
He added: "It's been a great honour. Last year we obviously had the Duchess herself, but we've both of them here this year so obviously a greater honour."
Drummer Steed said he had felt "proud" at leading Domhnall through the parade.
Speaking of the dog meeting the Duchess, he said: "She hooked the shamrock on to the collar, and then she patted him on the head and wished a happy St Patrick's Day.
"Thankfully he played the game."
He said the Irish Wolfhound Club of Ireland has donated a dog to be a mascot for the regiment since 1902.
"Domhnall and myself are basically the face of the battalion.
"On all state ceremonial occasions the battalion carry out, such as St Patrick's Day, Domhnall's always at the head of the parade, as well as meeting VIP visitors that come to camp on a daily basis."
