Czech and Slovak Federal Republic (Czech/Slovak: Česká a Slovenská Federativní/Federatívna Republika, ČSFR) was the official name of Czechoslovakia from April 1990 until December 31 1992, when the country was dissolved into Czech Republic and Slovak Republic.
While a return to the pre-1960 form Československá republika (Czechoslovak Republic) seemed obvious, Slovak politicians objected that the traditional name subsumed Slovakia's equal stature too much. The first compromise was Constitutional Law 81/1990, which acknowledged the state's nature explicitly as Československá federativní republika (Czechoslovak Federal Republic) in Czech and was passed on 29 March 1990 (coming into force on the same day) only after an agreement on the Slovak form as Česko-slovenská federatívna republika, to be explicitly codified by a future law on state symbols. This was met with general disapproval and another round of haggling, dubbed "the hyphen war" (pomlčková válka / vojna) after Slovaks' wish to insert a hyphen into the name à la Czecho-Slovakia, refused by aggrieved Czechs as too reminiscent of such practice during the "Second Republic" mutilated by the Munich Agreement and slipping toward fascism and final dismemberment. The resultant compromise after much behind-the-scenes negotiation was the Czech and Slovak Federal Republic (Constitutional Law 101/1990, passed on 20 April and in force since its declaration on 23 April; unlike the previous one, it also explicitly listed both Czech and Slovak version and stated they were equal).
Note that the name breaks the rules of Czech and Slovak orthography which does not use capitalization for proper names' second and further words (see above), nor adjectives derived from them. Thus the correct form would be "Česká a slovenská federat... republika" but Slovaks, having got a word of their own, refused to be deprived of a majuscule, while "Česká a Slovenská f. r." would imply a conjunction of two national republics, each having "federal" in its name; English-style capitalization of every word was adopted to hide this.
Few people were happy with the name, however it came into use quickly. Czecho-Slovak tensions, of which this was an early sign, soon became manifest in matters of greater immediate importance which made the country's name a comparatively minor issue and at the same time even more impossible to change, so it stayed until the final dissolution of Czechoslovakia.