The question as posed is difficult to answer for the following
reasons:
1) Does Jerusalem in another language count as another name of
Jerusalem? (i.e. does Jerusalén in Spanish count as another name
after Jerusalem in English?)
2) How common does a reference to Jerusalem have to be to be a
reference? (i.e. if 15 people use it, is it a name? How about
15,000? How about 15,000,000?)
3) Does the nickname have to apply exclusively to Jerusalem?
(i.e. can the name apply also to surrounding hill-country.
As a result it is difficult to give a figure with any
exactitude. Jews have upward 50 names for Jerusalem concerning its
various characteristics (i.e. Holy City, Old City, Davidic City,
Messianic City etc.). Muslims similarly have a large number of
names for Jerusalem concerning its various characteristics (i.e.
Holy City, Distant City, Respectable City etc.). Christians have
fewer such names, but they exist. When the linguistic issue is
opened up, these names just multiply.