Extracting medication names from handwritten doctor prescriptions is challenging due to the wide variability in handwriting styles and prescription formats. This paper presents a robust method for extracting medicine names using a combination of Mask R-CNN and Transformer-based Optical Character Recognition (TrOCR) with Multi-Head Attention and Positional Embeddings. A novel dataset, featuring diverse handwritten prescriptions from various regions of Pakistan, was utilized to fine-tune the model on different handwriting styles. The Mask R-CNN model segments the prescription images to focus on the medicinal sections, while the TrOCR model, enhanced by Multi-Head Attention and Positional Embeddings, transcribes the isolated text. The transcribed text is then matched against a pre-existing database for accurate identification. The proposed approach achieved a character error rate (CER) of 1.4% on standard benchmarks, highlighting its potential as a reliable and efficient tool for automating medicine name extraction.