Naming compounds with an OX group
The preferred IUPAC name (PIN) of the compound given in the question is butan-2-yl hypofluorite. It is named as ester of hypofluorous acid. In the seniority order of classes, esters are ranked between anhydrides and acid halides.
The corresponding subsection of the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) reads as follows:

P-67.1.3.2 Esters of mononuclear noncarbon oxoacids
Esters of mononuclear noncarbon acids are named in the same way as esters of organic acids (…). Alkyl groups, aryl groups, etc. are cited as separate words, in alphanumerical order when more than one, and followed by the name of the appropriate anion. Partial (acid) esters of polybasic acids are named by citing alkyl groups, aryl groups, etc. as separate words, in alphanumeric order if more than one, followed by the word ‘hydrogen’ (with the appropriate multiplying prefix, as necessary) also cited as a separate word, and the name of the appropriate anion. Salts of partial (acid esters) are named by citing the name of the cation before the name of the organic group; remaining acids groups are denoted by the word ‘hydrogen’ as described above. Structural specificity for esters of chalcogen analogues of mononuclear noncarbon oxoacids is provided by the appropriate italic element symbols O, S, Se, and Te, prefixed to the name of the group, as needed.