Thank you for clarifying that.

While there is bedtools window : https://bedtools.readthedocs.io/en/latest/content/tools/window.html it looks like you may be best served by using a custom program. Ask your favorite LLM for assistance if you don't program or I can post a solution suggested by GPT.

import pandas as pd
import sys

def main(file1_path, file2_path):
    # Load first BED file (with name column)
    df1 = pd.read_csv(file1_path, sep='\t', header=None, names=["chrom", "start", "end", "name"])

    # Load second BED file (no name column expected)
    df2 = pd.read_csv(file2_path, sep='\t', header=None, names=["chrom", "start", "end"])

    matches = []

    for _, row2 in df2.iterrows():
        chrom_matches = df1[df1["chrom"] == row2["chrom"]]
        for _, row1 in chrom_matches.iterrows():
            if abs(row2["start"] - row1["start"]) <= 100 and abs(row2["end"] - row1["end"]) <= 100:
                matches.append({
                    "chrom": row2["chrom"],
                    "start": row2["start"],
                    "end": row2["end"],
                    "matched_name": row1["name"]
                })
                break  # Stop at first match

    # Convert to DataFrame and print
    matched_df = pd.DataFrame(matches)
    print(matched_df.to_csv(sep='\t', index=False, header=False))

if __name__ == "__main__":
    if len(sys.argv) != 3:
        print("Usage: python bed_matcher.py <first_bed_with_name> <second_bed>")
        sys.exit(1)

    file1 = sys.argv[1]
    file2 = sys.argv[2]

    main(file1, file2)

Here is how you would run the program. (files as shown in the example in original question) :

python bed_matcher.py file1.bed file2.bed