Nomenclature of a tertiary amine
You have correctly identified the given compound as amine. Amines can be named in various ways. According to Subsection P-62.2.1.2 of the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book), the preferred IUPAC names (PINs) are formed by using systematic substitutive nomenclature. Primary amines are systematically named by adding the suffix ‘amine’ to the name of the parent hydride; secondary and tertiary amines are named by the same method with further N-substitution (see Subsection P-62.2.2.1).

When there is a choice among acyclic parent hydrides, a principal chain must be chosen. The first relevant criterion in this case provides that the principal chain has the greater number of skeletal atoms; i.e., the principal chain is the longest chain (see Subsections P-44.3 and P-44.3.2).

In this case, the longest chain has five carbon atoms; i.e. the unmodified parent hydride is ‘pentane’.

Addition of the suffix ‘amine’ and the corresponding locant to the name of the parent hydride yields the name ‘pentan-3-amine’.

Finally, the substituent prefix ‘methyl’, the multiplicative prefix ‘tri’, and the corresponding locants are added to express substitution by three methyl groups, which yields the name ‘N,N,3-trimethylpentan-3-amine’ (note that ‘N’ is lower than ‘3’).