Yes, because referring to a child by the name and pronouns they have requested will irreparably damage them. /s

It has been proven time and again, study after study, that acceptance and support for trans people of all ages improves their quality of life. In this case simply using the requested pronouns and name can have only positive effects on the child's life. Further gender affirming care has also been proven safe and effective. Hormones are generally not prescribed until after 16, and until then puberty blockers are proven to be both effective and completely reversible and 100% safe. They have been regularly prescribed to cis-children to manage conditions such as precocious puberty for decades. Their application to treat gender dysphoria is no different.

There is no good reason to withhold gender affirming care from a child that is showing signs of dysphoria. Witholding treatment only leads to greater risks of selfharm or suicide.