Are there cases when genus name is equal to the name of a higher taxon?
I answer for botany: no.

The International Code of Nomenclature for algae, fungi, and plants has strict requirements on names: 

Article 16.1 has:


  The name of a taxon above the rank of family is treated as a noun in the plural and is written with an initial capital letter. (...)


Article 18.1 has:


  The name of a family is a plural adjective used as a noun; it is formed from the genitive singular of a name of an included genus by replacing the genitive singular inflection (Latin -ae, -i, -us, -is; transcribed Greek -ou, -os, -es, -as, or -ous, and its equivalent -eos) with the termination -aceae (but see Art. 18.5)


And article 20.1 has instead:


  The name of a genus is a noun in the nominative singular, or a word treated as such, and is written with an initial capital letter.


On later article it is explained how to latinize names, with simpler rules (compared to Latin).  So genus are singular and higher rank are plural.

Additionally, for botanical nomenclature, an name for ranks between family and phylum rank is made usually by concatenating a genus name with some suffixes (which are rank specific, see article 16.3, 18.1). So reading a name, one could derive also the rank.  Just few families still have a old name, but still ending with 'ae' (e.g. Compositae, Cruciferae, etc., Art 18.5).  Now (just since 2011-2012 version) there are more exceptions in code, but for historical reasons and for names outside plants in stricter term.

Note: Some old names are automatically corrected with new rules (see e.g. 18.4), so we should have not equal names.