It is possible for someone to have an eating disorder without weight and body esteem issues (Sarkar, et al. 2013), but not Anorexia.
Fear of becoming fat or gaining weight and having a distorted view of themselves and of their condition are criteria required in the Diagnostics and Statistical Manual which is used for diagnosing mental health problems. Therefore, Anorexia would not be diagnosed without these criteria being present.
An eating disorder without body image issues would be diagnosed as EDNOS (Eating Disorder Not Otherwise Specified) under the 4th Edition, but as the 5th edition merged the former categories of Eating Disorders and Feeding Disorder in Infancy or Early Childhood and formed the new category, Feeding and Eating Disorders, the diagnosis under the 5th edition would be OSFED (Other Specified Feeding or Eating Disorder).
OSFED is every bit as serious as anorexia, bulimia, or binge eating disorder, and people suffering from OSFED are every bit as deserving and in need of treatment – their eating disorder is just presenting in a different way. It is common for symptoms to not fit with the exact diagnostic criteria for anorexia, bulimia, or binge eating disorder – OSFED accounts for a large percentage of eating disorders (Beat Eating Disorders, 2017).
Beat Eating Disorders (2017). Other Specified Feeding or Eating Disorder (OSFED). Retrieved from: https://www.beateatingdisorders.org.uk/types/osfed
Sarkar, S., Padhy, S. K., Rao, P., & Gupta, S. (2013). Transient eating problems in an adolescent without body image disturbances: a diagnostic quandary. Indian journal of psychological medicine, 35(4), 410. doi: 10.4103/0253-7176.122244 PubMed Central: PMC3868099