Jefferson's party was called the Republicans or the Democratic-Republicans. After the demise of the Federalist Party, just about everyone was a Republican for a short time, but then new splits developed with Andrew Jackson's supporters becoming known as the Democrats and the opponents of "King Andrew I" becoming the Whigs (most of whom later became Republicans when the new Republican Party was founded in the 1850s).
The Democrats claim to trace their history to Thomas Jefferson; the pre-Civil War Democrats may have been more in the Jeffersonian tradition than the Whigs were, but some of Jefferson's ideas had become accepted by everyone.