Use Czech Republic for biography of all time periods, unless the person is clearly associated with the state of Czechoslovakia. Follow the rule for Russia/Soviet Union/Former Soviet republic subdivision whenever possible.

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Examples

Former practice:
Dvorak, Antonin, 1841-1904.
Composers--Czechoslovakia--Biography.
Present practice:
Dvorak, Antonin, 1841-1904
Composers--Czech Republic--Biography.

Former practice:
Berg, Josef, 1927-
Composers--Czechoslovakia--Biography.
Present practice:
Berg, Josef, 1927-
Composers--Czech Republic--Biography.

Former practice:
Dubcek, Alexander, 1921-
Heads of state--Czechoslovakia--Biography.
Present practice:
No change.

Former practice:
Havel, Vaclav.
Presidents--Czechoslovakia--Biography.
Present practice:
Havel, Vaclav.
Presidents--Czechoslovakia--Biography.
Add: Presidents--Czech Republic--Biography.

but
Former practice:
Kafka, Franz, 1883-1924.
Authors, Austrian--20th century--Biography.
Present practice:
No change.