Is it permissible for an unmarried woman to imagine she is married to a man with Islamic characteristics or a religious scholar, or to imagine that a specific person she knows is secretly her husband, and is it permissible to mention the name of a specific man to herself?

If what you mentioned is imagining intercourse with a non-mahram man, then this is not permissible in Sharia. Ghusl (ritual bath) is required if it leads to the emission of semen, and Wudu (ablution) if it is madhy (prostatic fluid). However, if it is merely wishing to marry a man with certain characteristics, there is no harm in that according to Sharia.