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I know that this compound is named propanoyl chloride.
However I am not sure what to do when here are multiple -COX groups and they are of the highest seniority. There are two cases, when they are the same:
And when they are not:
For the first case I think it is called propanedioyl chloride, but I do not know what to do for the second. Is one of them cited as a prefix and if so which one?
Systematic names for acyl halides from suffix acids are formed according to Subsection P-65.5.1.1 of the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book).
P-65.5.1.1 Acid halides in which hydroxy groups of all acid groups expressed as the suffix denoting the principal characteristic group (carboxylic, sulfonic, sulfinic, selenonic, etc. acids) have been replaced by halogen atoms (F, Cl, Br, and I) are named by citing the name of the acyl group (…) followed by the name(s) of the specific class(es) as a separate word(s), in alphabetical order, each preceded by a multiplicative prefix, as needed.
Therefore, the preferred IUPAC name (PIN) for the examples given the question is ‘propanoyl chloride’, ‘propanedioyl dichloride’, and ‘propanedioyl chloride fluoride’, respectively.
However, note that various carboxylic acids were often given trivial names (e.g. reminiscent of their animal or vegetable origin), which are retained for general nomenclature (including functionalization).