Hello. Since "Prime Buyers" is your brand, and has a specific line, I think is best that you keep your "Prime look" on all other sub-mini-brands, starting with this one.
Since "prime time" usually starts at 7 a.m, I've made a little clock symbol over the letter "I" by respecting the symmetry with the other word. This is why I decided to make the logo in this way, by respecting the coloring and leaving the symbol over the "I" in "Prime".
Underneath, as you mentioned in the brief, I tried to integrate your name and make it look like a signature.
Do not hesitate to leave feedback. Any changes can be made.
If you want it to be even more personalized, we can try different types of hand writing.. or we could even insert your own hand writing as a signature.
To make the logo more centered and balanced, I've tried a different approach and combined the two symbols together. Please provide feedback. Thank you.