Name still appears in Facebook messenger after deactivting account

After deactivating my account people can still search for my name in messenger and our old conversations pop up. I am wondering, do you have to DELETE Your account so that this doesnt happen? And isntead name will say like Facebook User or something like that?

submitted by /u/sabermetricsformer
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Andy Nguyễn Group - mua bán fanpage facebook, mua bán group facebook, thuê group facebook, đổi tên fanpage, tăng like fanpage, mua like fanpage, bảo mật facebook, xác minh google maps, mua fanpage ad breaks
Website : mua fanpage
Hotline : 0977099016
Địa chỉ : 1185/5/1A Lê Văn Lương - Phước Kiển - Nhà Bè - HCM