If you have not done this yet run, don’t walk, to your nearest domain registry and register your name as a web domain. My favorite registry is Go Daddy.
Type your name into the box and see if it available. If it is buy it immediately. It should cost no more than $30.00 and will likely be much less.
If you have a common name type it in and add your initial. If it is still not available add dds to the end and or dr to the beginning. For example robertjonesdds or drrobertjones. Immediately buy any that are available. For now only consider domains with the dot com suffix. There are dozens of other options like dot co or dot net but the public overwhelmingly prefers dot com.
Don’t stop with your actual name but register your practice name and any variations you can think of.
Once you own a domain it is yours for life as long as you pay the annual registration fee. You can use it yourself or sell it in the future.
Have your web site provider set up a system so that all these domains will re-direct to your primary dental office site. You are not limited to one domain but can have any number all directed to one primary site.