This is very difficult for an ordinary Muslim like me to talk about things like this so I am just copying/paste from the following link.
Copied from here, please read this for details.
If something is not classified as haram (prohibited) in the Deen
(religion/way of life of a Muslim), then it is halal (permitted).
Retaining a name that (1) does not identify itself with/contain
anything Islamically forbidden and (2) is not a Name of Allah , has
not been declared haram.
It is according to sunnah (the examples of the Prophet's life what he
said, did, implemented, how he implemented), to change a bad name
(whether it is an arabic name or any other language) immediately, and
it is permissible according to sunnah to exchange a name for a better
According to Sheikh Muhammed Salih Al-Munajjid, "...if one's name is
Abdul-Messiah, for example, or similar such names, then he is
obligated to change it, as the Prophet had people with the names
Abdul-Ka'bah and Abdul-Uzzah change their names upon accepting Islaam.
If the original name does not comprise or imply anything forbidden in
Islaam, then he or she is permitted to retain it (such as the name
George, for example). As noted, though, it is preferable to change it
to an Islaamic name, as this also distinguishes him or her from the
While it is not haram to retain the name under the conditions listed
above, the muslim has a responsibility to the Sunnah of the Prophet ,
and is encouraged to choose "the best of names"; and the best of names
are the humblest, insha'Allah. In addition, the best of names we have
on this side of life, will be what we are called by in Paradise,
My understanding about your name:
Noah is the name of prophet so there should not be any issue with this name.
An English pronounciation is not an issue I believe as most Muslims take the name of our prophet Muhammad pbuh in their names but is usually spelt Mohammed which the English thought their are other variations used.using the English spelling or pronounciation does not invalidate the name.