What is the IUPAC name of [Co(NH3)5H2O]Cl3?
Multiplicative prefixes are not considered in determining the alphabetical order of ligands.
According to the current version of Nomenclature of Inorganic Chemistry – IUPAC Recommendations 2005 (Red Book), the systematic names of coordination entities are generated by using the following principles:

IR-9.2.2.1 Sequences of ligands and central atoms within names
The following general rules are used when naming coordination compounds:
(i) ligand names are listed before the name(s) of the central atom(s),
(ii) no spaces are left between parts of the name that refer to the same coordination entity,
(iii) ligand names are listed in alphabetical order (multiplicative prefixes indicating the number of ligands are not considered in determining that order),
(…)

Therefore, the systematic name of the coordination entity in $\ce{[Co(NH3)5H2O]Cl3}$ is “pentaammineaquacobalt” since the ammine ligands are named before the aqua ligand according to alphabetical order. Note that, since 1970, the recommended name for water $(\ce{H2O})$ as neutral ligand in coordination complexes is “aqua” (formerly “aquo”).
The ionic composition of the complex salt $\ce{[Co(NH3)5H2O]Cl3}$ may be indicated in several ways:

IR-9.2.2.4 Charge numbers, oxidation numbers and ionic proportions
The following methods can be used to assist in describing the composition of a compound:
(i) The oxidation number of the central atom in a coordination entity may be indicated by a Roman numeral appended in parentheses to the central atom name (including the ending ‘ate’, if applicable), but only if the oxidation state can be defined without ambiguity. When necessary a negative sign is placed before the number. Arabic zero indicates the oxidation number zero.
(ii) Alternatively, the charge on a coordination entity may be indicated. The net charge is written in arabic numbers, with the number preceding the charge sign, and enclosed in parentheses. It follows the name of the central atom (including the ending ‘ate’, if applicable) without the intervention of a space.
(iii) The proportions of ionic entities in a coordination compound may be given by using
multiplicative prefixes. (See Section IR-5.4.2.1.)

Therefore, correct systematic names for the compound $\ce{[Co(NH3)5H2O]Cl3}$ are:

pentaammineaquacobalt(III) chloride
pentaammineaquacobalt(3+) chloride
pentaammineaquacobalt(III) trichloride
pentaammineaquacobalt(3+) trichloride

Note that multiplicative prefixes are usually not used in binary names if there is no ambiguity about the stoichiometry of the compound.