KT88 is not a standard US tube designation using the
RETMA numbering system. GEC/Genalex, who developed the KT66 and KT88, had their own numbering system which didn't correspond with anyone else's (for example, their version of the 12AX7 was known as the B759). The KT stands for "Kinkless Tetrode", i.e. the beam-power configuration as originally used with the KT66 (aka 6L6). The KT88 was never given a RETMA designation in the US; instead, it's generally cross-referenced to Tung-Sol's 6550 (which used the 'industrial' numbering system, for whatever reason).
Before you ask about European tubes, they had a designation system of their own, which used a different coding. In their system, the filament voltage was indicated by the first letter, with E representing 6.3V. Note that said letter does not always denote a specific voltage; rather, the higher letters actually denote the filament
current, i.e. for tubes used in a series string a'la AA5 radios. The letters after the first designated the element(s) used inside the tube, with the numbers after the letters denoting the number in the series. For example, the EL34 has a 6.3V filament, contains a single power pentode section, and was designated number 34 in the series. More on these numbering systems (and others) can be found
here.
-Adam