To hallow anything is to set it apart as something special. So, to 'hallow God's name' means to thank Him and praise Him as the most special one in the universe. Biblically, a person's name means their character and authority and is not a simple label. So, the 'names' of the Lord refer to His very nature, particularly as revealed in Scripture. Hence, the best time to 'hallow His Name' is after reading Scripture. As You read your 10 chapters* ask the question 'What do I read about God that I can praise Him more?'. You are looking for aspects of His character that You can hallow and not technical titles that you can list out (such as all the Jehovah names of God). Try to focus on one aspect of His character that jumps out at you as you read Scripture.
When you have finished reading your 10 chapters* you should launch straight away into speaking aloud your thanksgiving and praise to God. You can use some of the verses you have read as helps to hallow His name by reading them out in a personalized way. For example, you have just read Ephesians and the aspect of God's character that strikes you is His Fatherhood. You can go back to Ephesians 1:3-5 and start by proclaiming something like, "My wonderful Heavenly Father I bless You, the Father of our Lord Jesus Christ. You have blessed me with every spiritual blessings in the heavenly place in Christ. Truly You are a good father who only blesses and You have chosen me to be holy and without blame in Your love, to be adopted as Your son! All praise to You my glorious Father.” You can continue by using Ephesians 1:17; 3:14; 4:6; 5:20 – try it now!
Let this stream of continuous thanksgiving and praise keep coming forth without stopping until You sense the Presence of God and your praise will transform into deep worship. You will know when this hallowing of His name turns to worship as your heart will melt and love and adoration for God will flow freely. In this place of worship the Lord will deal with Your heart as You meet with Him. This is the time You will come into repentance and consecration which is next step in the journey.
* 10 Chapters of the Bible a day is a recommendation and not a legalistic practice. I could also say read 30-40 minutes of the Bible a day. Basically, its reading big enough chunks of the Word to get the big story and the context and enough to soak in.