The general rule on the use of alcohol based perfumes/deodrants, etc is that if the alcohol has been extracted from grapes or dates their use will be forbidden since this is Najis (impure) and will thus make the body and clothes impure.
If the deodrants/perfume is made from synthetic/chemical alcohol, extracted and manufactured from items besides grapes or dates, then the use of such products is permissible. As a rule, ethanols are synthetic and hence permissible.
Hazrat Mufti M. Taqi Usmani Saheb, (A leading contemporary scholar of Pakistan) writes in his commentary of Sahih Muslim, "The majority of alcohol used in medication and perfumes is not manufactured from grapes and dates, it is extracted from grains, peels or petroleum etc." (Takmilah Fathul-Mulhim Vol. 3 Page. 608)
Allah SWT Knows Best