How do I match names if the first and last name of a table are in two columns?

Hello. I am taking data from two separate sources. One is from Fan Graphs which displays batter names (first and last) in one column and important stats of that batter in the next few columns. Another is taken from Fan Duel which has the first name in 1 column, the last name in the second column, and their salary in the 3rd column.

What I'd like to do is to merge these two tables together. The problem I'm having is when I do a filter to alphabetize them, they don't match up because there are more names on the Fan Duel Table and the last names in the Fan Graphs don't line up (for example, there are 5 Alex's, but when you compare the last names side by side, some of them don't line up because of shortcuts in nicknames, like instead of Alexander, it's Alex). You will see that in the example in the attachments. Now there are hundreds of batters here so I tried copying and pasting them and trying to line them up one by one but that took hours of work. This is something that I do on the daily: exporting these graphs so I can compare salaries and stats so copying and pasting is just too time consuming and doesn't give me time to analyze these charts.

I have heard that there is a way to set up a sheet where I can use a function that would allow me to match up the names even if they aren't exactly the same. The problem is I don't know how to do that, and I'm guessing it wouldn't be your standard function given that you need to match 1 column with two columns. I thought this would be the best place to ask to do that sort of thing. If I can program excel to match up these names together, it would definitely be easier for me to do a vlookup/index function to put the salaries and stats side by side, along with the names of the batters in one column.

Thanks for your help.