According to the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book), as already mentioned in the question, the name ‘disilazane’ is no longer recommended for $\ce{H3Si-NH-SiH3}$. Such structures are now named as amines. (Also note that the name ‘hexamethyldisilazane’ is ambiguous and therefore never was in accordance with IUPAC nomenclature.)
P-21.2.3.1 Heterogeneous parent hydrides composed of alternating heteroatoms, i.e., [a(ba)n hydrides], excluding carbon atoms and the halogen atoms.
Compounds containing an unbranched chain of alternating atoms terminated by two identical atoms of the element coming later in the seniority order O > S > Se > Te > N > P > As > Sb > Bi > Si > Ge > Sn > Pb > B > Al > Ga > In > Tl may be named by citing successively a multiplying prefix denoting the number of atoms of the terminal element followed by the ‘a’ term for that element, then the ‘a’ term of the other element in the chain and the ending ‘ane’. The terminal letter ‘a’ of an ‘a’ term is elided when followed by a vowel; the terminal vowel of a numerical prefix is not elided even when the ‘a’ term begins with the same vowel. When nitrogen atoms are present, amine names (see P-62) are preferred because of the higher functionality of amines. This concept does not extend to other elements. These parent hydrides are preselected parent hydrides (see P-12.2) and have priority to receive preferred IUPAC names, as long as they are used to name compounds containing carbon.
Symmetrical secondary amines are named according to Subsection P-62.2.2.1, which describes three different methods.
P-62.2.2.1 Symmetrical and unsymmetrical secondary and tertiary amines are named only by the same methods described in P-62.2.1.2.
(1) substitutively using the retained name ‘aniline’ or the suffix ‘amine’ and the name of a parent hydride with further N-substitution;
(2) substitutively, by prefixing, in alphabetical order when required, the name(s) of the substituent group(s) R, R' or R" to the parent hydride name ‘azane’. In order to avoid ambiguity, the second prefix in a secondary amine, and the second and the third prefixes in a tertiary amines must be enclosed in parentheses when these prefixes denote simple substituents.
(3) substitutively, by prefixing, in alphabetical order when required, the name(s) of the substituent group(s) R, R' or R" to the parent hydride name ‘amine’. In order to avoid ambiguity, the second prefix in a secondary amine, and the second and the third prefixes in a tertiary amines must be enclosed in parentheses when these prefixes denote simple substituents.
Method (1) generates preferred IUPAC names. Functional parent names like diethylamine and triethylamine are deprecated. The prefixes in names of such secondary and tertiary amines formed by method (2)[sic: read (3)] are set off by parentheses to distinguish them from these deprecated names.
The corresponding names for $\ce{H3Si-NH-SiH3}$ are actually given as examples in the Blue Book:
(1) N-silylsilanamine
(2) disilylazane
(3) disilylamine
(not disilazane; see P-21.2.3.1)
Note that, since $\ce{H3Si-NH-SiH3}$ does not contain any carbon, no preferred IUPAC name (PIN) is indicated in the Blue Book for this compound.
The corresponding names for the complete compound that is given in the question are:
(1) 1,1,1-trimethyl-N-(trimethylsilyl)silanamine
(2) bis(trimethylsilyl)azane
(3) bis(trimethylsilyl)amine
Since P-62.2.2.1 explicitly states that Method (1) generates preferred IUPAC names even for symmetrical amines, the preferred name for the complete compound that is given in the question is 1,1,1-trimethyl-N-(trimethylsilyl)silanamine.
