They that know, i.e. that thoroughly understand and duly consider. Thy name, i.e. thy nature and perfections, thy infinite power, and wisdom, and faithfulness, and goodness; which make a person a most fit and proper object for trust. The name of God is most frequently put for God, as he hath manifested himself in his word and works, as Deuteronomy 28:58 Psalms 7:17, Psalms 20:1 Proverbs 18:10, &c. Thou hast not forsaken; the experience of thy faithfulness to thy people in all ages is a just ground for their confidence. Them that seek thee, i.e. that seek help and relief from thee by fervent prayer, mixed with faith, or trust in God, as is expressed in the former clause.
Related Commentaries of Psalms 9:10
Psalms 9:10
10 And they that know thy name will put their trust in thee: for thou, LORD, hast not forsaken them that seek thee.