スーツケースを預かっていただけますか？って英語でなんて言うの？

Using the phrase "Is it possible to leave my suitcase here?" the person at the front of the lobby will understand that you want to leave your luggage here.
Following up this phrase you may use "I should be back by 3 pm". This will give the person waiting a time to expect your return.

After checking out of a hotel. you want to ask if they can keep your suitcase for a while. You also want to tell them the time you will be coming back to get it. Either of the above suggestions is adequate.

When talking about your bags you have with you when staying somewhere as well as calling it a 'suitcase' you can also use the term 'luggage'
'can i leave my suitcase here please' or 'would you look after my luggage please' are a polite way of asking someone

:Could I leave my suitcase here until ...pm?
>When asking someone for a favor (polite request), it's advised to use phrases such as ''could I/you...?, Would you mind....?, etc.

:Would you mind keeping an eye on my suitcase after checkout until ...pm? > keep an eye on... is a
common phrase we use to refer to watching someone or something. So here you are asking the
hotel clerk to look after your bags until a certain time.

If you would like to ask to leave your bag at the hotel and pick it up later you can use the sentences above.
Remember to let reception know what time you will be back, leave a contact detail in case they may need to get hold of you.
There should be no problem with the request and your bag will be stored away safely for you until you are back to pick it up.

"I am leaving my bag behind because I have no more room in my car, I will be back later to pick it up, is this okay?"

Using the word "would" to ask is polite. You can use the phrase "pick it up" to talk about when you will return for your suitcase. I hope that this helps. :)

When you want to ask someone if it you can leave a suitcase and return at a later time to pick it up, you can say "Would you mind if I leave my suitcase here and I'll come back and get it at...?"