How would I name O-methylations on sugars while retaining the sugar’s common name?
It is possible to name such compounds based on retained carbohydrate names in accordance with the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) as follows.

P-102.5.6 Monosaccharide derivatives
P-102.5.6.1 O-Substitution
In order to maintain the integrity of structures and take advantage of retained names to imply the absolute configuration, O-substitution is allowed in carbohydrate nomenclature. Substituents replacing the hydrogen atom of an alcoholic hydroxy group of a monosaccharide or monosaccharide derivative are denoted as O-substituents. The substitution of an anomeric hydroxy group is discussed in P-102.5.6.3.2. The O-locant is not repeated for multiple substitution by the same atom or group. Number locants are used as necessary to specify the positions of substituents; they are not required for compounds fully substituted by identical atoms or groups.
P-102.5.6.1.1 O-Acetyl and O-alkyl functionalization.
For O-acyl derivatives, names with the acid component cited as a separate word ending in ‘ate’ after the monosaccharide name are preferred to names using O-acyl group prefixes. However when the ose ending is changed (e.g. to denote a glycosyl or an acid function having seniority over an ester) O-acyl prefixes are required. O-Alkyl derivatives are always expressed by prefixes.

Therefore, the name for the corrsponding D-arabinose derivative with methyl substituents replacing the hydrogen atoms of two alcoholic hydroxy group is 2,4-di-O-methyl-D-arabinose.