The decision of a title is up to the queen to decide, although the new parents may also have a say.
A decree issued by King George V in 1917 limits the number of grand royal titles in a way that would make Harry and Meghan's son known as a "Lord" rather than as a prince. He wouldn't become "his royal highness" under the current rules.
The queen has the authority, however, to intervene as she did when William and his wife Kate started having children. The queen decreed that all of their children would be princes and princesses.
She could do the same for Harry and Meghan's offspring, but the queen's feelings on that subject haven't been made public.
It is also possible that Harry and Meghan could decide they don't want the special designation for the baby, in order to give their child a more normal upbringing.
The Associated Press contributed to this report.