In this use they are called reflexive pronouns.

These pronouns are called reflexive (that is, “bending back”) because they refer back to the subject and repeat its meaning in an object construction.

Note. A reflexive pronoun sometimes refers to a substantive in the objective case: as,—“Our captors left us to ourselves.”

In older English the simple personal pronouns me, thee, etc., were often used reflexively: as,—“I held me [= myself] still”; “Yield thee [= thyself] captive”; “They built them [= for themselves] houses” (see [§ 106]). This idiom survives in colloquial language (as, “I have hurt me,” “I have bought me a rifle”), but it is avoided in writing except in a few expressions such as: “I must look about me”; “We gazed about us”; “Look behind you.”

127. The adjective own is sometimes inserted between the first and the second part of the self-pronouns for emphasis.

Examples:

In this use, self is in strictness a noun limited by the possessive and by the adjective own, but the phrases may be regarded as compound pronouns. Other adjectives are sometimes inserted between the possessive and self: as,—my very self, his worthless self.

128. The intensive pronouns are sometimes used without a substantive. Thus,—