Learn Russian: Наша дочь не хочет быть дизайнером. - Our daughter does not want to be a designer.

When we talk about professions or roles using the verbs быть (to be) or стать (to become), Russian uses the Instrumental case. Since the noun дизайнер ends in a hard consonant, it takes the standard masculine Instrumental ending -ом to become дизайнером.

The daughter is female, so why does дизайнером have a masculine ending?

Many job titles in Russian, especially borrowed words like дизайнер, do not have a commonly used feminine form. The masculine form is used as a neutral professional title for both men and women. So, even though the subject (дочь) is feminine, the job title stays grammatically masculine.

I always forget how to conjugate хотеть (to want). Is хочет regular?

No, хотеть is a famously irregular verb because it mixes two different conjugation patterns! In the singular, it has a ч in the root and takes type-1 endings: я хочу, ты хочешь, она хочет. But in the plural, it keeps the т and takes type-2 endings: мы хотим, вы хотите, они хотят.

Why doesn't дочь end in -а or -я if it is a feminine noun?