Some new examples
- His success in the interview depends on the interviewer.
- He could do well in the interview, depending on the interviewer.
To understand the difference between depends in sentence (1) and depending on in sentence (2), we need to understand the grammar of the sentences.
In sentence (1) depends is a verb. It is the main verb in the sentence. The subject of depends is the noun phrase, his success in the interview.
In sentence (2) the main clause in the sentence is:
- He could do well in the interview
The main verb phrase in that clause is could do. The subject is he. The part at the end of sentence (2), depending on the interviewer, gives us extra information. It is not essential for the grammar, or for the meaning. This means that it is an adjunct. It is extra.
In sentence (2) depending on the interviewer is a preposition phrase. In this sentence depending looks like a verb - but it is not! It is a preposition. This preposition takes another preposition on as a complement. In example (2), the complement of on is the interviewer. This gives us one big preposition phrase:
- depending on the interviewer.
The Original Poster's question
We use depending on to add on extra information to a sentence or clause. We use the verb depend when we need to use a verb.
The Original Poster's examples both need the preposition construction depending on/upon. This is because they are adding extra information to a full clause. I have put the main clause in brackets, [ ], below:
[ The family name may appear on the left side or the right side of the door ] depending on which floor you are on.
[ A careful driver watches the road and goes slowly or quickly ] depending upon the condition of the road.
The part in bold tells us what the situation in the main clause depends on. We can divide the sentences into two parts, so that we have two sentences for each example:
[The family name may appear on the left side or the right side of the door ]. This depends on which floor you are on.
[ A careful driver watches the road and goes slowly or quickly ]. This will depend upon the condition of the road.
In the examples above, the word this refers to the situation which we described in the first sentence. The word this is the subject of the second sentences. So this time we use the verb depend not the preposition depending.
Hope this is helpful!