It does not appear that Éowyn is modeled after any specific individual. Some think that Éowyn could have been inspired by the women that would sneak into the war during WWI when Tolkien fought. Perhaps he knew personally a girl that had made a lasting impact on the outcome of his experience. Possibly a nurse, especially given Éowyn's declaration at the end of ROTK to "be a healer, and love all things that grow".
In his 2014 Thesis, Jon Michael Darga says,
By portraying Éowyn as an idealized woman at war, Tolkien expressly links her with
the wartime events surrounding England at the time that he wrote Rings, strengthening the notion that what Éowyn exemplifies is what modern women should strive for. Éowyn is a woman who wants to put in just as much work as the men; the women’s suffrage movement would still have been fresh in Tolkien’s mind, and in English factories “95 per cent of the workers were female, and they included not only all kinds of semi-skilled mechanics, gaugers, examiners and tracers, but also some fully skilled tradeswomen.” Éowyn is also a woman who disguises herself as a man to ride to war; protesting women during World War I often dressed as Joan of Arc and rode on horses during marches because Joan’s “transvestism and military vigilance... subverted the order of femininity... she was and was not a woman... [transcending] the limitations of her sex and... [posing] a challenge to the English and to men... She offered an identification which was neither that of the domestic feminine ideal nor of its obverse, the hysterical fanatic.” [sic]
Tolkien’s Women: The Medieval Modern in The Lord of the Rings
So unlike Lúthien, the common interpretation of Éowyn is more symbolic, rather than based on someone in Tolkien's life.