In America, Kathy is a very, very common name for women in their 50's and 60's. For women 30-40, you'd more commonly hear 'Katie.' They are shortened forms of 'Katherine,' although, 'Kathy' can also be a shortened form of 'Kathleen.'

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According to the US Social Security Administration, in the year 2000, "Katherine" was the 37th-most-popular baby name. So women in their early twenties named "Katherine" would not be at all rare. "Kathy" would probably be the most common nickname for "Katherine" (although there are many others, including Kat, Katy, Katie, Kay, and Kit). And there is also the popular name Catherine and its nicknames, including Cathy, Cathie, etc. A few years ago a mutual fund manager named Cathie Wood was all over the financial news because her mutual fund had done really well. So, my answer is "no." It may not be among the most common, but it is very common and hardly "out of fashion."

Out of style where? It is used in so many countries. The name is common in every European language.