We have not found the name Ffayy in the sources available to us, therefore we do not know what its meaning is, so we cannot issue a ruling on it. Unless its origin is the word fay', and the final hamzah has become assimilated into the ya' that precedes it. Fay' means a shadow. However it cannot be imagined that the first letter (fa') could be doubled in Arabic at all!
Names such as this, that are not known as names and are not used among Muslims should be avoided altogether when naming one's children. Coming up with strange things is not praiseworthy with regard to names and it may lead to negative consequences in the future for the person who is given this name.
Whatever the case, we have previously listed some important guidelines for naming by boys and girls and what should be avoided. Please see the answer to questions no. 7180 and 101401. Whoever follows these guidelines and avoids what is warned against will be safe from anything that is contrary to shareeah in sha Allah.
And Allah knows best.
Reproduced from Islam QA