How to create new group by condition from another column in dataframe?

Question

So I have this kind of data

data = [['A', 0], ['A', 1], ['A', 2], ['A', 15], ['A', 2], ['A', 12],['B',1],['B',3]]
df = pd.DataFrame(data, columns = ['name', 'interval'])

    name    interval
0   A       0
1   A       1
2   A       2
3   A       15
4   A       2
5   A       12
6   B       1
7   B       3

so I want to create a new name based on the interval (if the interval>10 then the new name is generated) but still using the previous name like this (this is just an example name)

    name    interval    new_name
0   A       0           A_0
1   A       1           A_0
2   A       2           A_0
3   A       15          A_1
4   A       2           A_1
5   A       12          A_2
6   B       1           B_0
7   B       3           B_0

My current code is accessing every row using for, any other idea to process it? Thank you

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Credits to Rutger for his idea. This is the flow how to do it

    name    interval    condition  cumsum   new_name(name+"_"+cumsum)
0   A       0           False      0        A_0
1   A       1           False      0        A_0
2   A       2           False      0        A_0
3   A       15          True       1        A_1
4   A       2           False      1        A_1
5   A       12          True       2        A_2
6   B       1           False      0        B_0
7   B       3           False      0        B_0

Details of the code is in the Rutger's answer

Answer 1

I think the easiest is to start with creating a bool series and then create your new field like this:

df['large_interval'] = 10 < df['interval']
df['new_name'] = df['name'] + '_' + df.groupby('name')['large'].cumsum().astype(str)

On the second line it counts how many large intervals have passed per group. That value is used as a string and added after then name and _.