(written from a Production point of view)
Tycho Crater is a prominent crater, named for Tycho Brahe, on the Moon. It was mentioned (though misspelled Tycho Carter) in a portion of the Picard family album that did not make it on screen. There it appeared on an invitation for the wedding of Beverly Howard and Jack Crusher, the ceremony for which was to take place at the rim of the crater. Its possible that it gave its name to such Lunar locations as Tycho City and Tycho Base.