How can you come up with a good name for your home school? Some people opt for keeping it simple. They may use (last name) Home School or (street name) Home School or (geographical feature) Home School. These options work well if you are not actually going to share your school name with anyone, however emblazoning (name) Home School or (street name) Home School on school T-shirts, for example could be a privacy issue for your child depending on their age and where they wear the shirt.
Another possibility for the less creative is to use a name generator. AOPS and Eclectic Homeschooler both have them. The names they generate can be silly but they may give you a jumping off point. Is "Heritage Family Academy" too country for you? Try "Faith Christian Academy" instead. Is it too stuffy or too religious? Maybe "Oakwood School" would be better.
If you have older children, it may be fun to involve them in the decision making.
This brings up an important point, which is that your child will need to list their home school name on all kinds of applications in the future, so as fun as "(family name) School for the Criminally Insane" sounds now, you might want to pick something that sounds professional and respectable for future reference. Also, remember that it can create a bad impression , or possibly create a legal trademark dispute, if you use the name of another school as your own. In other words, calling your school "Harvard University" is a really bad idea. A quick internet search can help you avoid this type of trouble. If you just really love a name, you might add a geographical designation to clearly distinguish your school from the more famous one--ie. "Columbia Homeschool of the Everglades".
Finally, remember, like many things in home schooling, your school name can usually be changed (unless it is on a diploma) if doesn't work for you.