Melchizedek is the same person as Adonizedek. Joshua is the same person as Jesus.
H3091
יהושׁע יהושׁוּע
yehôshûa‛ yehôshûa‛
yeh-ho-shoo'-ah, yeh-ho-shoo'-ah
From H3068 and H3467; Jehovah-saved; Jehoshua (that is, Joshua), the Jewish leader: - Jehoshua, Jehoshuah, Joshua. Compare H1954, H3442.
G2424
Ἰησοῦς
Iēsous
ee-ay-sooce'
Of Hebrew origin [H3091]; Jesus (that is, Jehoshua), the name of our Lord and two (three) other Israelites: - Jesus.
Mat 1:21 And she shall bring forth a son, and thou shalt call his name JESUS: for he shall save his people from their sins.