In recent years, image has become the most popular format for digital data sharing. Unlike the common image formats such as JPEG, medical images uses special image formats like DICOM. The integrity among the medical image and a patient's identity is undividable for any diagnostic purpose in medical application. This can be achieved by embedding the patient's personal details as invisible watermark on their medical images. As one's personal information needs to be kept confidential, performing encryption on watermark information can serve this purpose. Edges are considered as vital regions in medical images as it contains precise information required for diagnostic purpose and referred as region of interest. This paper suggests a method for the insertion of encrypted watermark on DICOM image via LSB embedding procedure to provide ownership identity and authentication. The proposed method preserves the edge information in the cover image by inserting the watermark only on non edge pixels of the cover image. Besides the encryption, additional security is given to watermark information via the randomness obtained from the PRNG in the selection pixel positions for watermark embedding. The proposed algorithm was implemented using Python. The analysis performed on the watermarked DICOM image through standard metrics such as MSE, PSNR and SSIM confirms the imperceptibility of the embedded watermark information.