Yes, but ....... In the Isle of Man women, including married women, did not lose their property and civil rights to the extent that these were lost in England from the end of the middle ages to the reforms (divorce, married women's property act, extension of the franchise) of mid C19 to early C20.

It seems to have been common practice to recognise both names throughout, though not universal. Women from long-established Manx families or very rich ones were more likely to find their birth surname still in use decades after they married.

Well into my lifetime it was common for a woman from such a family to be referred to in formal documents - protocols laid down by the English! - by her husband's surname but to be referred to in conversation by her birth surname. It did not happen to my mother because she came from "across" and, therefore, the locals had no knowledge of her family and/or its relative standing in its own community.

With wills in Scotland it still common practice to say "the last will and testament of me Margot X, wife (or widow) of Charles Y"

In other words, it is not wise to read across directly from the UK to the Isle of Man. Both the law and common usage are different.