Minimalist Logo Design for Product Packaging + Online Shop for Medjool dates

Need to create simple logo for dates online shop, the domain name is Medjool.pl and I would like to creat something similar to the first attachment Medjool plus mp, so I used canvas and edited it a bit as you see in the second attachment. I got stock at the last step, in which the letter L gowing down from the letter M needs to be red. as the dot in the j letter. I am also looking for inspiration while keeping the same design, font as attached.

Main wording (Medjool.pl)
Main colors ( black, white, red)