Many of the 15 had already formalised declarations of independence before the legal dissolution of the USSR.
The parliament of Ukraine had already declared independence in August
Eastern Germany had joined up with West Germany in October 1990.
In 1991 and 1992, Yugoslavia broke up into Croatia, Slovenia, Macedonia and Bosnia and Herzegovina.
In December 1992, Czechoslovakia split into the Czech Republic and Slovakia.
Kosovo declared independence in 2008 but is only partially recognised by the UN with Russia, China, Serbia and others still seeing it as part of Serbia.
Well worth visiting the capitals of Estonia, Latvia & Lithuania. They are proudly independent but the situation is complicated by having a lot of Russian speakers in the eastern parts. Also they only have populations of about 2 million each – so if they weren’t part of NATO, Russia could invade them in an afternoon.