Why did Marich in Ramayana took the name of Lakshman first though he was not prepared to do so nor was he told to act so by Ravana and also why did he utter them after he was shot By Lord Rama?

This was an evil plan of Ravana. Although Marich was unwilling to become a golden deer, Ravana forced him to accept that role. He conspired a plan to abduct Mother Sita. He explained to Marich how he should allure mother Sita by his graceful feats and when she wants to have that wonderful dancing golden deer, he should play hide and seek with Lord Rama. When Lord Rama follows it, let Him go more deep in the forest. He knew that Lord Rama will not allow mother Sita to be alone anytime and He shall ask Lakshman to protect Her from dangers in the forests. When Lord Rama shoots an arrow to kill him, he should call out, “O Sita!, O Lakshman!” imitating the sound of Lord Rama. When Lakshman thinks that His brother is in difficulty, He shall leave mother Sita alone to go to help Him. This is the time, when Ravana shall come to execute his evil plan.