Excel search for certain text within cell and return vlookup from a range

In Table 1 I have a column of Names in one tab (column H) and would like to bring in the Contact information (column I) based on a list (columns A and B) in a separate tab (Table 2). Table 1 example:

List Table 2 example:

I would like my original Table 1 to look like this Table 3 example:

The issue I'm encountering is that it's looking only for an exact match of contents of the full name cell (even when I use "X" wildcard). Is there a way to search for just specific text within the cell (e.g., BMI within a cell even though the cell says BMI Properties) and return as a vlookup or something, the value in the adjacent cell? Thank you for your help! I've searched extensively and nothing works.

Here is one way of achieving the desired output:

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=MAP(A2:A4,LAMBDA(α, FILTER(E2:E4,1-ISERR(FIND(" "&D2:D4&" "," "&α&" ")))))

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Similarly, can use XLOOKUP() as well:

=MAP(A2:A4,LAMBDA(δ,XLOOKUP(1,1-ISERR(FIND(" "&D2:D4&" "," "&δ&" ")),E2:E4)))

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Please ensure to change the cell range and reference as per your suit.

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Also since you mention in the OP, you are using Structured References then use it in the following way:

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=XLOOKUP(1,
 1-ISERR(FIND(" "&Table2[If Name contains the following text]&" "," "&[@Name]&" ")),
 Table2[Contact Info])

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If have access to REGEXTEST() can test as well, this works on my end:

=XLOOKUP(TRUE, 
 REGEXTEST(A2,"\b"&Table2[If Name contains the following text]&"\b"),
 Table2[Contact Info],"None")

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