Multiple matches in comma separated list

The core of this formula is the IF function, which "filters" the names in the table by color like this:

IF(group=E5,name,""))

The logical test checks each cell in the named range "group" for the color value in E5 (red in this case). The result is an array like this:

{FALSE;FALSE;TRUE;TRUE;FALSE;FALSE;TRUE}

That result is used in turn to filter names from the named range "name":

{"Matt";"Sally";"Jude";"Aya";"Elle";"Linda";"George"}

For each TRUE, the name survives, for each FALSE, IF returns an empty string ("").

The result of IF looks is this array:

{"";"";"Jude";"Aya";"";"";"George"}

which goes into the TEXTJOIN function as text1.

TEXTJOIN is configured to use a comma as the delimiter, and to ignore empty values. The final result is this text string:

"Jude, Aya, George"

Line break instead of comma

To join matches with a line break instead of a comma, you can adjust the formula like this:

=TEXTJOIN(CHAR(10),TRUE,IF(group=E5,name,""))

The CHAR function returns the code used for a line break. You will also need to enable text wrapping.

Multiple conditions

You can't use the AND or OR functions in an array formula like this because they only return a single result. You can use boolean logic like this for AND:

=TEXTJOIN(", ",TRUE,IF((condition1)*(condition2),name,""))

Explained in more detail here.