What is the proper name for the but-1-ene's isomer methylpropene?
Generally, the complete information about a structure is explicitly given by the name and does not rely on any implied information. Nevertheless, the practice of omitting locants when there is no ambiguity is widespread in general nomenclature. For preferred IUPAC names, however, locants are omitted only in a few exceptional cases described in Subsection P-14.3.4 of the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book).
Ignoring the rules for omission of locants, the complete systematic name of the parent compound would be ‘prop-1-ene’. According to Rule P-14.3.4.2, however, the locant ‘1’ is omitted. (Note that no other isomer can be generated by moving the double bond from its position to another.)

P-14.3.4.2 The locant ‘1’ is omitted:
(…)
(d) in unsubstituted dinuclear and trinuclear alkenes and alkynes and monounsaturated cycloalkenes and cycloalkynes; (…)

Thus, the preferred IUPAC name for the unsubstituted parent structure is propene.
Ignoring cis/trans isomerism, the substitutable hydrogen atoms of propene have three different locants (‘1’, ‘2’, and ‘3’). Therefore, the locants for substituent prefixes (e.g. ‘1-chloro’, ‘2-chloro’, or ‘3-chloro’) cannot be omitted in substituted propene.
Since, the locants for the substituent prefixes cannot be omitted, also the locant ‘1’ of ‘prop-1-ene’ can no longer be omitted for preferred IUPAC names.

P-14.3.3 Citation of locants
In preferred IUPAC names, if any locants are essential for defining the structure of the
parent structure or of a unit of structure as defined by its appropriate enclosing marks, then all locants must be cited for the parent structure or that structural unit. (…)

For example, (1E)-1-chloroprop-1-ene, (1Z)-1-chloroprop-1-ene, 2-chloroprop-1-ene, and 3-chloroprop-1-ene are the preferred IUPAC names for some substituteded propenes.
This principle applies to any substituent. The special situation that replacing the chloro substituent in (1E)-1-chloroprop-1-ene, (1Z)-1-chloroprop-1-ene, and 3-chloroprop-1-ene with a methyl substituent would actually lead to the names (2E)-but-2-ene, (2Z)-but-2-ene, and but-1-ene instead of ‘(1E)-1-methylprop-1-ene’, ‘(1Z)-1-methylprop-1-ene’, and ‘3-methylprop-1-ene’, respectively, does not change the preferred name for 2-methylprop-1-ene. (Note that the substitutable hydrogen atoms of propene have three different locants irrespective of the kind of the substituent.)
Therefore, the preferred IUPAC name is 2-methylprop-1-ene.