Pivot Sum of Multiple Columns

I have an excel table that I use for calculating values for a project. For a few reasons I've had to lay things out in a way that makes it difficult to set up a pivot table to show what I want it to, but I feel like it should be possible to do.

I've attached a small basic example of what I'm working with, and what I would like to see and so far Google hasn't shown anything promising.

Basically I have a large table with a few input columns and multiple formula columns. But the pertinent part here is two columns that have formulas to generate a value based on some of those inputs. In the example I attached, this would be the name columns. Both of those columns have their own quantity columns as well. The number columns in the attached example. Sometimes there are blanks in a row in either of those columns and I don't really care what happens with those. Sometimes the columns have matching values in the same row and sometimes they don't. Some values may exist in one column and not the other. What I would like to do is have a table like the output table in the attached example that would give me a sum of the corresponding quantities for each unique value across those two columns. I can't really predict very well what the values may be and they are always subject to change so I can't do SUMIF(S) with a table, so I feel like I'm stuck with a Pivot Table to avoid having to expand the output ranges and manually input the names it looks for. I'm not very familiar with Pivot Tables yet, so I'm open to suggestions if there is a better option here.

Product information says Microsoft Excel for Microsoft 365 MSO Version 2406, but I have had issues with a few functions not working that I believe should with my version of Excel so there's that. There's also little consistency through the company with what version of Excel my coworkers have, so compatibility with older versions would be nice but not necessary as this will be used by me only 99 percent of the time.

Thank you so much. With a little bit of tinkering, I was able to make that work for what I need. Only drawback is that it's already past the end of the day and now I'm going to be at the office for several more hours figuring out where else I can use this new knowledge.

G3=IFERROR(SUMPRODUCT(--(Table1=Table2[@Name]),($B$3:$E$12)),"")

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