When we partake of the sacrament, we renew that covenant to take upon us His name and make additional promises to improve. Our daily thoughts and actions, both large and small, reflect our commitment to Him.
Elder Ronald A. Rasband, "Be Not Troubled", Deseret Book 2021
"Always remember Him" doesn't necessarily mean Christ is always at the forefront and focus of every single thought. Like we can't think of anything else. We couldn't fulfill our mortal responsibilities that way. We couldn't focus on anything else that way. It's just not feasible.
He should be, however, behind the "intent" of every single thought, as well as, every single action. In other words, every single thought we have and every single action we take, should be done as if He were right there participating with us in them.
The way we live our lives is a direct manifestation to Him of our intent or commitment to Him. He will know by our thoughts and actions of our loyalty and love for Him. He knows our thoughts and actions anyway, but through those, we show and express to Him, where we are trying to end up. Where our desires are.