London — Now that everyone knows Prince Harry and his wife Meghan have a baby boy, there is widespread speculation about what he will be called. Royals have a way of taking their time about naming babies and the couple is known to want to do things at their own pace, so it may be a few days before the couple reveals the name for their first child.

Britain's legal bookmakers Tuesday reported high interest in the names Alexander, James, Philip and Arthur. Bookmakers also report speculation about the name Spencer, the maiden name of Harry's late mother, Princess Diana.

There was speculation, meanwhile, that the royal birth didn't go completely according to plan. As CBS News contributor Tina Brown, author of "The Diana Chronicles," told "CBS This Morning" on Tuesday, there were unconfirmed reports that Meghan was rushed to a hospital either early Monday or late Sunday, in spite of her hopes for a home birth. The palace would not immediately comment on the reports.

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Either way, both mother and son were said to be doing well, and that left royal watchers around the world to speculate on the child's name on Tuesday.

Choosing Spencer as a first or middle name is seen as a way for Harry to honor Diana, who died in a Paris car crash in 1997 when he was only 12. He spoke before he married Meghan last year about his desire to pay tribute to her memory during the ceremony.

Others believe Meghan, the Duchess of Sussex, will choose a name that reflects her American heritage.

The infant, known only as Baby Sussex for the moment, was born early Monday morning.

Harry said when he announced the birth Monday that he and Meghan were "thinking" about names and hinted that an announcement might be made on Wednesday on shortly thereafter. The couple is also expected to pose with their newborn or release a photo on their Instagram account.

The couple is also expected to name godparents to the child at a future date.