The common name of a plant
People often give plants names of their own. These are called "common names". "Apple tree" is the common name for Malus pumila. "Apple" in Italian is "mela", in Russian " яблоко", in Norwegian "eple", and in Japanese "ringo". But to a botanist in any of these countries, it is known as Malus pumila. By having the same agreed upon name, botanists avoid the potential confusion of common names.
There is nothing wrong with common names, in fact they are important. They should be coupled with their corresponding botanical name to avoid confusion especially if you are doing a landscape design or looking for specific information about a plant.
Common names are not capitalized unless the name is a proper noun. California bay is spelled with an upper case "C" because California is a proper noun and lower case "b" in "bay" because it is not a proper noun. The common name for Laurus nobilis is sweet bay; spelled with all lowercase letters because neither sweet nor bay are proper nouns.