Concerning the name Allah this is from a christian blog:
The normal generic word for God is "alaha"/"aloho" (ܐܠܗܐ), which is linguistically related to the Hebrew word for God "elohim".
The translation of the tetragrammaton, YHWH, on the other hand, is "maria"/"morio" (ܡܪܝܐ), usually decomposed as mar-yah, Lord-Yah ("mar", lord, also being used by syriac speaking churches as a title for saints/doctors of the Church: "mor Ephrem" = Saint Ephrem). (Note: this word has nothing to do with the proper name Maria, coming from the Hebrew Mariam)
To answer your question, Jesus would almost certainly have used one of the two, or both at the same time as it is commonly done in Syriac: Maria Alaha.
Last remark: The arabic word Allah, used also by Arabic Christians, is no more no less related to the Aramaic Alaha than to the Hebrew Elohim. The three share a common linguistic root, which is nothing exceptional, so no point being dragged on sterile arguments concerning this point.
