Seaborn: Is there a better way to wrap the text in my bar plot?

I am writing a function for bar plots and have encountered another small problem. I have some ytick labels that are too long, causing my y axis label not able to be seen. I'm only able to see the y label when I drastically decrease the size of the ytick labels.

def bar_plot(data, x, y, title):
    sns.set_style('darkgrid')
    data = data.sort_values(ascending=False, by=x)
    data = data.head(n=10)
    if (data[x]>1000000).any():
        data[x] = data[x] / 1000000
        ax = sns.barplot(data=data, x=x, y=y)
        ax.set_title(title, size=35)
        ax.set_xlabel(x + ' ($ Millions)', size=15)
        ax.set_ylabel(y, size=15)
        ax.set_yticklabels(data[y].head(n=10), wrap=True)

    else:
       ax = sns.barplot(data=data, x=x, y=y)
       ax.set_xlabel(x, size=15)
       ax.set_ylabel(y, size=15)
       ax.set_title(title, size=35)
       ax.set_yticklabels(data[y].head(n=10), wrap=True)

I have tried ax.set_yticklabels(data[y].head(n=10), wrap=True) to wrap the text. While it works, it doesn't wrap the text enough. Is there a way to tell wrap=True to wrap after x amount of characters? I've tried googling this but couldn't quite find anything that works.

Edit

The format of the dataframe that I am working with is similar to

Client Name            Col 1      Col 2      Col 3      Col 4       Col 5
Some name              51,235.00  nan        23,423.00  12,456.00   654.00
Some long company name 152.00     5,626.00   nan        82,389.00   5,234.00
Name                   12,554.00  5,850.00   1,510.00   nan         12,455.00
Company                12,464.00  nan        752.00     1,243.00    1,256.00
Long Company Name      12,434.00  78,915.00  522.00     2,451.00    6,567.00

from Seaborn: Is there a better way to wrap the text in my bar plot?