At least over in the States, that is a phenomenon that pretty much occurred from the 30s - 60s. Over here, that sort of thing is usually still done by young couples who live in large urban cities, where still many put up posters of favorite stars and favorite movies on front room walls.
Long ago, some fathers used to call their sons John Wayne _____. Women usually got their first names (Jeanette - Jeanette MacDonald, Marilyn - Marilyn Monroe, etc). When on a recent family visit, we were watching an interview with the singer Bette Midler and she said that she and her sisters were all named after famous actresses. She was named after Bette Davis. Although, her mom pronounced it Bet; while Miss Davis pronounced it, Betty.
Per British actors and actresses, Once met a young Rachel Ward. Tiffany and Audrey, after the "Breakfast at Tiffany's", the shop, and actress were popular names between 60s and 80s. Audrey Hepburn still has the cosmo influence over here on many cosmo women. Emma is a great name and has made a come back in recent years. Emma Thompson may have some influence here. Some girls may have been named after Kate Winslet, also. As they were twin popular in the 90s in a big way - Chick Lit/Flick phenmomenon. Here, Elizabeth Taylor probably has had the biggest name influence from a British actor or actress over the years.
A lot of kids were named after the Beatles in the 60s, etc. Ironically, the West Coast Muslim terrorist John Walker Lindh was named after John Lennon. And, thank Heaven the hippie age is over: Moon Unit, Zowie - poor kids. It's telling that David Bowie's son renamed himself.
My niece is named after the Royal Borough, Chelsea, which has been popular in the past decade or so. Not after a film, but a lot of movies have been filmed there. :)
Film stars aside, a lot of little girls have been named after Lady Diana. See a lot of Di's and Dee Dees coming up the road. Also, many women named Elizabeth, after I & II, Elizabeth Taylor, family or movie. This is a name that doesn't rust. It's like the word fresh (as in always).
By and large, I think the "aristocratic age" of the star is passing and people are generally going back to naming children after family or friends. Most men in my family through the centuries have typical English men's names: John, George, William, Henry, etc., and one or two Old Testament names, which was a Puritan phenomen that lasted from the 1600s - 1800s. Although, that has revived amongst many Evanglicals, since the 70s. The ancient Hebrew names refer to character.
Women family names have been more elegant: Grace, Letitia, Emma, Amie. One favorite was my g-g-g grandmother - her name was Sophia Wayne, pronounced similarly to the singer Shania Twain.
Gibbie
P.S - Summer funny, Freddy. I read where Winston Churchill was once asked where the Virgin Islands were; he responded, "the farthest away from the 'Isle of Man.'" :)