1: Forget var even exists. var was deprecated 7 years

Question

1: Forget var even exists. var was deprecated 7 years

ago. Use const or let instead. (This is the third time today I have to say this....)
2: Use classes instead of prototypes or constructor functions. I assume you are using constructor functions due to self
3: Know your types. Will patientName ever be null? Or will it be the empty string? One of the conditions is likely unnecessary. Switch to TypeScript to make this easier
4: Don't mix code fetching data from the DOM with code processing data
5: Avoid using IDs to get data from the DOM. It leads to every part of the program having to know what IDs everything else is using, to avoid duplicates. This in turn leads to loads of unnecessary complexity
6: Name your functions properly. getTabSubTitle doesn't even get anything. I would expect a getter to return something. This is a glorified setter, which reads data from the DOM.
7: Make functions which have one, and only one, responsibility. getTabSubTitle is responsible for checking if a given name exists, read from the DOM, and update some state
8: Use template strings for making a string from variables: `${firstName} ${lastName}`