You have raw rows on one side and a clean summary on the other. This fills the summary in, adding up every row that belongs to each name.
The formula
=SUMIFS(B:B,A:A,D2) in column E
=SUMIFS(B:B,A:A,D3) in column E
What each part does
SUMIFS
Adds numbers only from the rows where every condition is true.
B:B
The numbers being added.
A:A, D2
Keeps only the rows where A:A equals whatever is in D2.
How it works, and what to watch for
The name in the summary is what SUMIFS matches against, so as you fill the formula down it lines up with each name in turn.
Keep the raw data and the summary in separate columns, or a stray match will quietly inflate a total.
If a total looks too low, the names probably do not match exactly, a trailing space is the usual reason.
Questions
How is this different from a pivot table?
A pivot table is quicker for a one-off look. A formula updates itself the moment the data changes and sits right beside your other columns, which is often what you want in a live sheet.
Can I total by two things at once, say name and month?
Yes, add another pair to SUMIFS: the second range and the second thing to match. That is exactly what SUMIFS is built for.
Set by your computer's language, not by the file. A frequent cause of a correct-looking formula being rejected.
Excel version
XLOOKUP, IFS, TEXTBEFORE and TEXTJOIN need Microsoft 365 or 2021; older versions return #NAME? instead. Choosing the older one switches every walkthrough to a formula that works there.