Choosing what to call plants is often a challenging decision for gardeners because sometimes it seems we speak different languages when referring to the same thing. From my grandmother, I learned that the big yellow flowers with dark brown centers are called Black-Eyed Susans. They were among the first flowers I planted as an adult. When I became serious about gardening and first entered conversations with expert gardeners, I was confused when they talked about the Rudbeckia in their gardens. It turns out Rudbeckia hirta and Black-Eyed Susans are the same plant.
Some gardeners, usually ones with specialized training, prefer to use the scientific name for plants. That includes the genus and species; it's a precise taxonomic description with Latin as the base. Scientific names are recognized by national and international organizations and are consistent for a plant regardless of the location of the garden. Many other gardeners prefer to use common names. Common names use common language to identify a plant, though those names may vary by region or country.
My gardener friends Diane, Cathie, and Carol can sit and talk at length about visiting nurseries and seeing plants. They talk about catalogs and new varieties and new opportunities. They use the scientific Latin names and understand everything they say to each other. To me it's virtually a foreign language, but I admire and am envious of their knowledge.
I do try to expand my vocabulary and understanding by learning the scientific names for many of the plants I grow so that I can converse appropriately. I memorized Centranthus ruber because that was one of my favorite plants; that's "Jupiter's Beard" or "Red Valerian" depending on where you come from. I'll talk about my Echinacea more than I will my Coneflowers (they're the same thing). I grow Penstemon and talk about them that way, though others call them "Beard Tongue." Agastache is a common xeric plant in our part of the country and I knew it by that name before I heard of "Giant Hyssop."
Where names become problematic is when you want to share information with another gardener or with a nursery worker. If you are talking about something that the other person doesn't understand, communication breaks down. You both may know about a specific plant, but if you can't identify it with an appropriate name common to the two of you you might as well be speaking different languages (which you really are).
Using a translator is a great idea. I like the "National Garden Book" published by Sunset Books. It includes an encyclopedia of plants that lists them by both common and scientific names. Last summer my good friend Diane asked if I wanted some of her Achillea, Calendula, and Delosperma for my new beds. Of course I said yes. Then I went home, looked them up in my book and found out I was getting Yarrow, Marigold, and Ice Plant.
Neither the common nor the scientific names are "the best" way to identify plants. My usage is relative to the situation at hand. When speaking about plants with my wife, daughter, or most people I know, I use the common names. That's how they know them. When I talk to fellow Master Gardeners or people I know prefer a scientific name, I'll do the best I can to pepper the conversation with my limited knowledge of Latin. If I don't know the plants they're talking about, I've learned to ask for clarification; it helps me learn.
I recommend learning the scientific names if you're serious about gardening. It's not for you to show off, but rather so you can communicate with other serious gardeners and gardening resources. Many locals know that the state flower of Colorado is a Columbine, the "Rocky Mountain Columbine" to be precise. If you want to grow it in your garden you might have trouble finding the seeds or plants if you didn't know to look for Aquilegia caerulea. Knowing that Columbines are Aquilegia is a good start, but there are many species: Aquilegia alpina is the "Alpine Columbine", Aquilegia chrysantha is the "Golden Columbine", and Aquilegia vulgaris is the "European Columbine". If you're looking for a specific flower in a specific color or size, you'll need to know the complete scientific name.
I'll continue to use the common names for most of my conversation and plant tags, but will expand my name awareness at every opportunity. Many popular catalogs list plants by common names, especially with vegetables and fruits, which makes ordering easy. Our local nurseries are mixed, with many of their plant tags only listing the scientific name. If I know what I'm looking for I don't have to ask for a translation from an employee, but more often than not I need help.
For most gardeners it's about the process of gardening and not the name of the plant. We know what we like and what we want to grow. We may not know what a plant is called, but if we want it we'll find out. Whether we use the common name or the scientific name only matters to the person supplying the first plant to us. Beyond that you can call it whatever you like.