The 23-year-old reality TV personality has been dating Goldstein, a disc jockey who goes by the name DJ AM, for one year. The couple recently moved into a Hollywood Hills home together, and they are still working on merging their styles, Richie tells PEOPLE.
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Richie, the adopted daughter of R&B star Lionel Richie, is currently co-starring with hotel heiress Paris Hilton on the third season of The Simple Life, and is working on her own debut album.
No date for the nuptials has been announced.