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"Multiples" would include 10000 ("myriad"), 10^100 ("googol"), 10^(10^100) ("googolplex") and maybe 100000 ("lakh") and 10000000 ("crore"). None of these are powers of 1000 (as in the companion sequence A060366). - Robert Dawson, Mar 28 2020

Since the use of alphabetic names is rare for numbers greater than 10^15, there is no universal agreement on the naming scheme for large integers, and there is some question whether this sequence would well-defined without the "less than 10^303" clause.

The Wikipedia article compares 8 dictionary sources and has names for the powers of 1000 up to 10^63 and for 10^303. These are also in the Mathworld link.

There are several conflicting schemes for extending the dictionary definitions. If we assume that the system of alphabetic names greater than 10^63 defines a word for every power of 1000 and that word comes before "vigintillion" alphabetically, the sequence can include all integers. However, many of the extension schemes listed do not meet that standard - some have multiple words and some have words that are alphabetically after "vigintillion".

For the powers of 1000 between 10^66 and 10^303, one source (http://www.mrob.com/pub/math/largenum.html) coins the name "vigintinonillion" for 10^90, but this format is inconsistent with other names listed in the same source, e.g. "duovigintillion", "sexoctogintillion". The name "novemvigintillion" seems to be more common. Otherwise, all sources have "vigintillion" as alphabetically last of all the powers of 1000 up to 10^303.

The terms are from Andrew Weimholt.