In Matthew 1:21 what is the name of Jesus in the Peshitta text? Is it the same as the name given in Luke 3:29, Acts 7:45 and Hebrews 4:8 which is rendered as Joshua in English?
Dr. Sebastian P. Brock, who retired from teaching at Oxford University, has demonstrated that the Peshitta New Testament was translated from the Greek into Syriac. The name of Jesus in the Syriac Peshitta text is ܝܫܘܥ (Jesu). This is how it is rendered in Matthew 1:21. However, the name 'Joshua' is not consistently rendered in this way in Syriac, presumably because it was not consistently rendered in the Greek.
In Luke 3:29, Joshua is transliterated as ܝܘܣܐ (Jose). Yet in Acts 7:45, Joshua is rendered the exact same way as Jesus (ܝܫܘܥ). This is most likely because in Luke 3:29, the Majority/Byzantine Greek text uses Ἰωσῆ (Jose) while in Acts 7:45 the Greek text uses Ἰησοῦ (Jesus).
Hebrews 4:8 is a peculiar case because most Greek manuscripts render this as Ἰησοῦς (Jesus), and the Syriac Peshitta also does (ܝܫܘܥ). However, the Syriac also has ܒ݁ܰܪ ܢܽܘܢ (son of Nun, בַּר נוּן) (clearly referring to Joshua, not Jesus). It seems that this may be a scribal gloss added for clarification, although the reasoning behind this gloss would be better suited as its own question. Modern translations almost unanimously translate this passage as referring to Joshua, but the King James Version rendered it as 'Jesus.'