Traditionally, wines have been named after the primary grapes used to make the wine and the location where those grapes were grown--a region or a specific vineyard. This is still the case in historic wine-making areas like Bordeaux and Burgundy. "New world" wines, from areas without a long history of wine making, tend to have brand names--less descriptive but often more creative, like the popular Australian label Yellow Tail. Hobbyist wine makers can consider both methods when naming a homemade wine.
Start with the grapes used to make your wine. Pinot noir, chardonnay and cabernet sauvignon are known as varietals. If your wine features a particular varietal, consider incorporating it into the name. Bonny Doon Vineyard's Syrah Le Pousseur is an example of a wine made primarily from the syrah grape. If it's a special blend, you could also indicate that in the name by calling it a "vintner's blend," like Abacela Vintner's Blend #10 from Oregon.
Consider the geographic area where your grapes were grown. Depending on where you live, your grapes may be from a known wine region like the popular California winery, Gallo of Sonoma, or from an up-and-coming area, like the Texas Hills Vineyard. Including the geographic location in the wine name could be reassuring, if the grapes are from an area that people are familiar with, or fun, if the wine is from an unusual place.
Think about including the vineyard name if all the grapes came from one. The famous Bordeaux wine, Chateau Mouton-Rothschild, is named after the wine estate where the grapes are grown and the wine is produced. French wine makers use the word "terroir" to describe a grape's character as a result of the soil in which it's grown. If you feel the terroir gives your wine its essential character, this is an idea for a name. Particularly if you grew the grapes yourself (even if your "vineyard" is your backyard), it would be meaningful to associate the wine with the land where the grapes were grown.
Brainstorm words that describe your wine or your personality. Don't think about it too much, just have fun with the process. A brand name can be anything--serious, silly, romantic, sentimental or idiosyncratic. For example, the California wine, Marilyn Merlot, imparts an instant impression of the winemaker's sensibility. Even though you're making the wine for personal consumption, it's good to have a name that conveys meaning about the wine.
Compile all the ideas you've just collected: the varietal, geographic region, vineyard and branding notes. Write them down and play around with the words in various configurations. From these concepts you'll be able to create a name for your wine.
These suggestions are for the amateur winemaker making wine for personal consumption, not the commercial vintner. If you are making wines for commercial sale, you must research the local and federal laws about wine labeling and trademarks.