I want to be a psychologist but I worried if it is haram to use secular therapy methods and treat non-Muslims with these methods without using remembrance in Allah and Islamic practices as part of the therapy?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Psychological treatment is permissible in principle, and it is not necessary for the treatment of psychological diseases to be by way of Ruqyah and the like.

Psychological diseases are like organic diseases: it is legislated and permissible to seek treatment for them by all permissible means that have been proven beneficial by experience, such as taking medicines, or cognitive and behavioral treatments.

Allah knows best.